U.S. patent application number 13/840664 was filed with the patent office on 2014-08-07 for apparatus and method for defining coupled systems on spatial dimensions and extra dimensions.
This patent application is currently assigned to Comsol AB. The applicant listed for this patent is COMSOL AB. Invention is credited to Daniel Bertilsson, Eduardo Fontes, Eduardo Gonzalez, Lars Langemyr, Nils Malm, Arne Nordmark, Johan Ojemalm, Niklas Rom, Hans Rullgard, Henrik Sonnerlind, Johan Thaning.
Application Number | 20140222384 13/840664 |
Document ID | / |
Family ID | 51259989 |
Filed Date | 2014-08-07 |
United States Patent
Application |
20140222384 |
Kind Code |
A1 |
Nordmark; Arne ; et
al. |
August 7, 2014 |
APPARATUS AND METHOD FOR DEFINING COUPLED SYSTEMS ON SPATIAL
DIMENSIONS AND EXTRA DIMENSIONS
Abstract
A simulation apparatus for adding extra geometries to a model of
a physical system. The apparatus is configured to modify a geometry
of a model of a physical system represented in terms of a combined
set of equations. Instructions on the apparatus cause one or more
processors to perform, upon execution, acts comprising: (i)
receiving a base geometry of the physical system, (ii) receiving
one or more extra geometries associated with the base geometry,
(iii) determining first geometric entities of the base geometry and
second geometric entities of the extra geometry, (iv) adding the
extra geometries to the base geometry by computing a product
geometry of the determined first geometric entities and the second
geometric entities, (v) generating an updated combined set of
equations including representations of the product geometry, and
(vi) generating a graphical representation of the product geometry,
the graphical representation configured for display on the display
device.
Inventors: |
Nordmark; Arne; (Stocksund,
SE) ; Fontes; Eduardo; (Vallentuna, SE) ;
Rullgard; Hans; (Nynashamn, SE) ; Sonnerlind;
Henrik; (Ekero, SE) ; Ojemalm; Johan; (Solna,
SE) ; Langemyr; Lars; (Stockholm, SE) ;
Bertilsson; Daniel; (Vallentuna, SE) ; Malm;
Nils; (Lidingo, SE) ; Thaning; Johan; (Arsta,
SE) ; Gonzalez; Eduardo; (Stockholm, SE) ;
Rom; Niklas; (Vallentuna, SE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
COMSOL AB |
Stockholm |
|
SE |
|
|
Assignee: |
Comsol AB
Stockholm
SE
|
Family ID: |
51259989 |
Appl. No.: |
13/840664 |
Filed: |
March 15, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61760504 |
Feb 4, 2013 |
|
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|
Current U.S.
Class: |
703/1 |
Current CPC
Class: |
G06F 30/23 20200101 |
Class at
Publication: |
703/1 |
International
Class: |
G06F 17/50 20060101
G06F017/50 |
Claims
1. A simulation method executed in a computer system with one or
more processors configured to modify a geometry of a model of a
physical system including physical quantities represented in terms
of a combined set of equations, the simulation method comprising
the acts of: defining geometry data representing a geometry of a
physical system represented by a first combined set of equations,
said geometry data associated with a first model of said physical
system; defining, via one or more processors, extra geometry data
representing one or more extra geometries for a modified model
based on said first model; determining, via at least one of said
one or more processors, a first set of geometric entity data
representing one or more geometric entities of said geometry of
said physical system from which to extend said one or more extra
geometries; adding, via at least one of said one or more
processors, at least a portion of said extra geometry data
representing at least one of said one or more extra geometries to
said determined first set of geometric entity data representing one
or more geometric entities by forming product geometry data
representing a product geometry for said modified model, said extra
geometry data representing said one or more extra geometries being
at least a part of said product geometry data; generating, via at
least one of said one or more processors, non-discretized equation
data representing a non-discretized second combined set of
equations for at least a portion of said product geometry data; and
optionally generating a graphical representation of at least a
portion of said product geometry data, said graphical
representation configured for display on a graphical user
interface.
2. The method of claim 1, wherein said graphical representation
includes said at least a portion of said product geometry data.
3. The method of claim 1, wherein an extra dimension includes said
one or more extra geometries.
4. The method of claim 1, further comprising the act of:
determining, via at least one of said one or more processors, a
second set of geometric entity data representing one or more
geometric entities of said one or more extra geometries; and
determining product selection data representing a product of
selections computed as a Cartesian product between at least a
portion of said first set of geometric entity data representing one
or more geometric entities of said geometry and at least a portion
of said second set of geometric entity data representing one or
more geometric entities of said one or more extra geometries.
5. The method of claim 1, wherein said non-discretized equation
data representing said non-discretized second combined set of
equations are user editable to allow editing of said second
combined set of equations.
6. The method of claim 1, wherein said non-discretized second
combined set of equations are a combined set of non-discretized
partial differential equations configured as input data for a
partial differential equation solver.
7. The method of claim 1, wherein at least one of said one or more
geometric entities is a vertex.
8. The method of claim 1, wherein at least one of said one or more
geometric entities is an edge.
9. The method of claim 1, wherein at least one of said one or more
geometric entities is a boundary.
10. The method of claim 1, wherein at least one of said one or more
geometric entities is a domain.
11. The method of claim 1, further comprising the act of defining
material property data representing a material property for at
least one of said one or more extra geometries.
12. The method of claim 1, further comprising the act of: after
forming said product geometry data representing said product
geometry for said modified model, defining material property data
representing a material property for at least a portion of said
product geometry data.
13. The method of claim 1, wherein said geometry of said physical
system is one-dimensional and said one or more extra geometries are
two-dimensional.
14. The method of claim 1, wherein said geometry of said physical
system is three-dimensional and said one or more extra geometries
are one-dimensional.
15. The method of claim 1, wherein said geometry of said physical
system and said one or more extra geometries are
three-dimensional.
16. The method of claim 1, wherein said determining of said first
set of geometric entity data representing one or more geometric
entities on said geometry of a physical system is based on user
selections received via a graphical user interface.
17. The method of claim 4, wherein said determining of said second
set of geometric entity data representing one or more geometric
entities of said one or more extra geometries is based on user
selections received via a graphical user interface.
18. The method of claim 1, wherein said defining said geometry data
representing said geometry of said physical system includes
extracting said geometry data from data representing said first
model of said physical system.
19. The method of claim 1, wherein said defining extra geometry
data representing one or more extra geometries occurs at least in
part via selections of extra geometry properties received via a
graphical user interface.
20. The method of claim 4, wherein said defining extra geometry
data representing one or more extra geometries occurs at least in
part via selections of extra geometry properties received via a
graphical user interface.
21. A simulation system for adding extra geometries to a base
geometry of a model of a physical system represented in terms of a
combined set of differential equations, the system comprising: one
or more physical memory devices; one or more display devices; one
or more user input devices; and one or more processors configured
to execute instructions stored on at least one of the one or more
physical memory devices, the instructions causing at least one of
the one or more processors to performs steps comprising defining
base geometry data representing a base geometry of a physical
system, said base geometry data associated with a first model of
said physical system, said physical system represented by a
combined set of differential equations, defining extra geometry
data representing one or more extra geometries for a modified model
based on said first model, determining a first set of geometric
entity data representing one or more entities of said base geometry
from which to extend said one or more extra geometries, adding at
least a portion of said extra geometry data representing at least
one of said one or more extra geometries to said determined first
set of geometric entity data representing one or more entities of
said base geometry by generating product data representing a
product geometry for said modified model, said extra geometry data
being at least a part of said product data, generating equation
data representing an updated combined set of differential equations
for said modified model that includes said at least a portion of
said product data, and storing said equation data and said product
data in at least one of said one or more physical memory
devices.
22. The system of claim 21, wherein at least a portion of said
product data is stored as graphical representations configured for
later display on said one or more display devices.
23. The system of claim 21, wherein the instructions cause at least
one of the one or more processors to further perform a step
comprising generating a graphical representation of at least a
portion of said product data, said graphical representation
configured for display on at least one of said one or more display
devices.
24. A simulation apparatus for adding extra geometries to a model
of a physical system, the apparatus comprising: a physical
computing system comprising one or more processors, one or more
user input devices, a display device, and one or more memory
devices, at least one of the one or more memory devices including
executable instructions for modifying a geometry of a model of a
physical system represented in terms of a combined set of
equations, the executable instructions causing at least one of the
one or more processors to perform, upon execution, acts comprising
in response to one or more first inputs received via said one or
more user input devices, receiving a base geometry of said physical
system, said base geometry associated with a model of said physical
system represented in terms of a combined set of equations,
receiving one or more second inputs via at least one of said one or
more user input devices, said second inputs defining one or more
extra geometries associated with said base geometry, determining
one or more first geometric entities of said base geometry and one
or more second geometric entities of said extra geometry, adding at
least one of said one or more extra geometries to said base
geometry by computing a product geometry of said determined one or
more first geometric entities and said one or more second geometric
entities, said one or more extra geometries being at least a part
of said product geometry, generating an updated combined set of
equations including representations of at least a portion of said
product geometry, and generating a graphical representation of at
least a portion of said product geometry, said graphical
representation configured for display on said display device.
25. The apparatus of claim 24, wherein said updated combined set of
equations is a combined set of non-discretized differential
equations.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims priority to and the benefits of U.S.
Provisional Application No. 61/760,504, filed on Feb. 4, 2013, the
disclosure of which is hereby incorporated by reference herein in
its entirety.
FIELD OF THE INVENTION
[0002] The present invention relates generally to methods and
apparatus for modeling and simulation, and more particularly, to
techniques for modeling and simulation on a computer system that
include defining physical systems on spatial dimensions and extra
dimensions.
BACKGROUND
[0003] Computer design systems are used to develop product designs
and may include graphical user interfaces. Computer design systems
can be complemented with packages analyzing a single aspect of a
design, such as, structural analysis in conjunction with
computer-aided design systems. It would be desirable to have design
systems that can operate in more complex environments.
SUMMARY OF THE INVENTION
[0004] According to one aspect of the present disclosure, a
simulation method executed in a computer system with one or more
processors is configured to modify a geometry of a model of a
physical system including physical quantities represented in terms
of a combined set of equations. The simulation method comprises the
acts of defining geometry data representing a geometry of a
physical system represented by a first combined set of equations.
The geometry data is associated with a first model of the physical
system. Extra geometry data representing one or more extra
geometries for a modified model based on the first model is
defined, via one or more processors. A first set of geometric
entity data representing one or more geometric entities of the
geometry of the physical system from which to extend the one or
more extra geometries is determined via at least one of the one or
more processors. At least a portion of the extra geometry data
representing at least one of the one or more extra geometries is
added, via at least one of said one or more processors, to at least
a portion of the determined first set of geometric entity data
representing one or more geometric entities by forming product
geometry data representing a product geometry for the modified
model. The extra geometry data representing the one or more extra
geometries is at least a part of the product geometry data.
Non-discretized equation data representing a non-discretized second
combined set of equations for at least a portion of the product
geometry data is generated via at least one of the one or more
processors. Optionally a graphical representation of at least a
portion of the product geometry data is generated. The graphical
representation is configured for display on a graphical user
interface.
[0005] According to another aspect of the present disclosure, a
simulation system for adding extra geometries to a base geometry of
a model of a physical system represented in terms of differential
equation comprises one or more physical memory devices, one or more
display devices, one or more input devices, and one or more
processors configured to executed instructions stored on at least
one of the one or more physical memory devices. The instructions
cause at least one of the one or more processors to perform steps
comprising defining base geometry data representing a base geometry
of a physical system. The base geometry data is associated with a
first model of the physical system, which is represented by a
combined set of differential equations. Extra geometry data is
defined representing one or more extra geometries for a modified
model based on the first model. A first set of geometric entity
data is determined representing one or more entities of the base
geometry from which to extend the one or more extra geometries. At
least a portion of the extra geometry data representing at least
one of the one or more extra geometries is added to the determined
first set of geometric entity data representing one or more
entities of the base geometry by generating product data
representing a product geometry for the modified model. The extra
geometry data is at least a part of the product data. Equation data
is generated representing an updated combined set of differential
equations for the modified model that includes at least a portion
the product data. The equation data and the product data is stored
in at least one of the one or more physical memory devices.
[0006] According to yet another aspect of the present disclosure, a
simulation apparatus for adding extra geometries to a model of a
physical system. The apparatus includes a physical computing system
comprising one or more processors, one or more user input devices,
a display device, and one or more memory devices. At least one of
the one or more memory devices includes executable instructions for
modifying a geometry of a model of a physical system represented in
terms of a combined set of equations. The executable instructions
cause at least one of the one or more processors to perform, upon
execution acts comprising receiving a base geometry of the physical
system in response to one or more first inputs received via the one
or more user input devices. The base geometry is associated with a
model of the physical system which is represented in terms of a
combined set of equations. One or more second inputs are received
via at least one of the one or more user input devices. The second
inputs define one or more extra geometries associated with the base
geometry. One or more first geometric entities of the base geometry
and one or more second geometric entities of the extra geometry are
determined. At least one of the one or more extra geometries are
added to the base geometry by computing a product geometry of the
determined one or more first geometric entities and the one or more
second geometric entities. The one or more extra geometries are at
least a part of the product geometry. An updated combined set of
equations is generated including representations of at least a
portion of the product geometry. A graphical representation is
generated of at least a portion of the product geometry. The
graphical representation is configured for display on the display
device.
[0007] According to further aspects of the present disclosure, one
or more non-transitory computer readable media are encoded with
instructions, which when executed by one or more processors
associated with a design system, a simulation system, or a modeling
system, causes at least one or the one or more processors to
perform the above methods.
[0008] Additional aspects of the present disclosure will be
apparent to those of ordinary skill in the art in view of the
detailed description of various embodiments, which is made with
reference to the drawings, a brief description of which is provided
below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] Features and advantages of the present disclosure will
become more apparent from the following detailed description of
exemplary embodiments thereof taken in conjunction with the
accompanying drawings in which:
[0010] FIGS. 1A-1E illustrate an exemplary flowchart and wizard for
the creation of a base model, according to some aspects of the
present disclosure.
[0011] FIG. 2 illustrates an exemplary a table of terms for
geometric entities in different space dimensions, according to some
aspects of the present disclosure.
[0012] FIGS. 3A-3B illustrates exemplary menus for adding a physics
interface and study to a base model, according to some aspects of
the present disclosure.
[0013] FIGS. 4A-4C illustrate an exemplary a flowchart and wizard
for the creation of an extra dimension, according to some aspects
of the present disclosure.
[0014] FIGS. 5A-5C illustrate exemplary menus for features related
to an extra dimension, according to some aspects of the present
disclosure.
[0015] FIGS. 6A-6B illustrate exemplary menus, tools, and graphical
representations for creating extra geometries, according to some
aspects of the present disclosure.
[0016] FIG. 7 illustrates an exemplary a flowchart for creating a
product geometry, according to some aspects of the present
disclosure.
[0017] FIGS. 8A-8D illustrate exemplary menus, tools, and graphical
representations for selections of base geometry entities and extra
geometries, according to some aspects of the present
disclosure.
[0018] FIG. 9 illustrates an exemplary a flowchart for creating a
product of selections, according to some aspects of the present
disclosure.
[0019] FIGS. 10A-10E illustrate exemplary menus and graphical
representations for the product of selections tool, according to
some aspects of the present disclosure.
[0020] FIG. 11 illustrates an exemplary settings window for
defining variables for products of selections, according to some
aspects of the present disclosure.
[0021] FIGS. 12A-12B illustrate exemplary menus and a settings
window for defining an operation on a product of selections,
according to some aspects of the present disclosure.
[0022] FIG. 13A-13C illustrate exemplary menus and a settings
window for defining material properties on a product of selections,
according to some aspects of the present disclosure.
[0023] FIGS. 14A-14B illustrate exemplary materials selection tools
for layered structures, according to some aspects of the present
disclosure.
[0024] FIGS. 15A-15C illustrate exemplary menus and a settings
window for adding weak contributions to a product of selections,
according to some aspects of the present disclosure.
[0025] FIGS. 16A-16B illustrate exemplary menus and a settings
window for adding a weak constraint to a product of selections,
according to some aspects of the present disclosure.
[0026] FIGS. 17A-17B illustrate an exemplary menus and a settings
window for adding a pointwise constraint to a product of
selections, according to some aspects of the present
disclosure.
[0027] FIGS. 18A-18B illustrate an exemplary menus and a settings
window for adding an auxiliary dependent variable to a product of
selections, according to some aspects of the present
disclosure.
[0028] FIG. 19 illustrates an exemplary menus and a settings window
for defining a mesh on a product of selections, according to some
aspects of the present disclosure.
[0029] FIG. 20 illustrates exemplary equations and parameters
describing modeled reactions, according to some aspects of the
present disclosure.
[0030] FIG. 21 illustrates exemplary equations describing physical
properties of species in the bulk of a modeled reactor, according
to some aspects of the present disclosure.
[0031] FIG. 22 illustrates an exemplary equations describing
physical properties of species in the porous particles of a modeled
reactor, according to some aspects of the present disclosure.
[0032] FIGS. 23A-23C illustrate exemplary menus and settings
windows for creating geometries describing a bulk reactor as a base
geometry and particles as an extra geometry, according to some
aspects of the present disclosure.
[0033] FIGS. 24A-24B illustrate exemplary settings windows for
defining parameters and variables in a physics interface for
modeling a reactor including porous particles described as an extra
geometry, according to some aspects of the present disclosure.
[0034] FIG. 25-29 illustrate exemplary settings windows for a bulk
reactor and in porous particles included in the reactor, according
to some aspect of the present disclosure.
[0035] FIG. 30 illustrates an exemplary a plot of concentrations
along the reactor length of a modeled reactor, according to some
aspect of the present disclosure.
[0036] FIG. 31 illustrates exemplary expressions describing
absorption and scattering of radiation in a participating media,
according to some aspect of the present disclosure.
[0037] FIG. 32 illustrates an exemplary computer system, according
to some aspect of the present disclosure.
[0038] FIG. 33 illustrates exemplary systems that may reside and be
executed in one of the hosts of FIG. 32, according to some aspect
of the present disclosure.
[0039] While the present disclosure is susceptible to various
modifications and alternative forms, specific embodiments have been
shown by way of example in the drawings and will be described in
detail herein. It should be understood, however, that the invention
is not intended to be limited to the particular forms disclosed.
Rather, the invention is to cover all modifications, equivalents,
and alternatives falling within the spirit and scope of the
invention as defined by the appended claims.
DETAILED DESCRIPTION
[0040] While this invention is susceptible of embodiment in many
different forms, there is shown in the drawings and will herein be
described in detail preferred aspects of the invention with the
understanding that the present disclosure is to be considered as an
exemplification of the principles of the invention and is not
intended to limit the broad aspect of the invention to the aspects
illustrated. For purposes of the present detailed description, the
singular includes the plural and vice versa (unless specifically
disclaimed); the words "and" and "or" shall be both conjunctive and
disjunctive; the word "all" means "any and all"; the word "any"
means "any and all"; and the word "including" means "including
without limitation."
[0041] Exemplary methods, systems, and apparatus for constructing
geometries for models of physical systems, and forming product
geometries between base geometries and extra geometries are
described. The contemplated geometries can be of various dimensions
and the forming or computing of a product geometry includes
Cartesian products. Further exemplary aspects of the present
disclosure contemplate defining physical properties, physical
quantities, parameters, variables, and boundary conditions on such
products, or portions thereof, that are further applied to describe
a model of a physical system as a combined system of equations. In
additional exemplary aspects of the present disclosure, the model
is discretized and provided as a system of equations to an equation
solver that solves the system of equations and provides a useful
solution to an operator of a modeling or simulation system.
[0042] The exemplary aspects described herein can be particularly
useful and provide a computational advantage for methods, systems,
and apparatus for modeling and simulation of physical systems.
Physics interfaces for modeling and simulation systems, such as
physics and multiphysics modeling systems, include systems that
provide for specific dimensionalities of geometries for the
physical systems being modeled. Typical dimensions of geometr(ies)
for a physical system that is being modeled include dimensions
between zero and three. Some physics interfaces include systems for
modeling on geometries of specific dimensions. For example, shell
physics interfaces include systems for modeling surfaces embedded
in three dimensions, or beam physics interfaces include systems for
modeling line segments embedded in three-dimensions. Additionally,
some physical systems that are the subject of modeling are
described by a phase space that includes a higher dimensionality
than three. For example, in describing spatial and velocity
distributions of a gas, three dimensions can be applied for
describing position and three dimensions for describing the
velocity. It is contemplated that modeling such a system can
include describing or defining the velocity as a field with values
in each position with each value of the field representing a
velocity density in that respective position.
[0043] It is contemplated that it would be desirable for a modeling
system to represent or define geometries of physical systems as
base geometries and to also be able to define one or more extra
geometr(ies). For example, in some aspects, it can be desirable for
a model of the spatial and velocity distribution of gas to include
representing the spatial distribution as a three-dimensional
geometry, also referred to as a base geometry, and to represent the
velocity distribution as another three-dimensional geometry called
an extra geometry. The phase space can then represented by a
Cartesian product or product geometry of at least some of the
geometric entities of the base geometry and some or all of the
geometric entities of the extra geometry. Geometric entities can be
understood as being at least a part or portion of a specific
dimension of the geometry for a model.
[0044] A Cartesian product or product geometry is exemplified as an
operation that can be implemented between two sets of data, in this
case geometry data, by forming all possible combinations of
objects, or geometric entities, in one set of data with objects, or
other geometric entities, in the other set of data. For example,
assuming a first set of data is represented by Y={1, 2, 3} and a
second set of data is represented by Z={a, b, c}, the following
outcome is an exemplary product geometry of the two exemplary sets
of data: [0045] Y.times.Z={(1, a), (1, b), (1, c), (2, a), (2, b),
(2, c), (3, a), (3, b), (3, c)}.
[0046] A formation of a product geometry between multiple sets of
geometry data that represent physical systems of a model can be
observed in different ways. For example, in some aspects, on a set
of non-discretized geometries or geometric entities, a product
geometry can be formed that includes all tuples of such
non-discretized geometries or geometric entities. When implemented
on a modeling system, such a product geometry can create either
tuples of identifiers or some sort of indexes for the geometries or
geometric entities or pointers to such identifiers or indexes. It
is also contemplated in some aspects that a Cartesian product can
be expressed in setting the start and end conditions for several
nested loops or similar algorithm operations for creating such
tuples.
[0047] In some aspects of a multiphysics modeling system, including
modeling systems identified elsewhere herein, systems of coupled
partial differential equations ("PDEs") may be discretized using
finite elements in a base geometry and in the geometry in the extra
dimension, which are associated with model(s) of a physical system.
A Cartesian product of two sets of discretized geometries can
include all tuples of the mesh element points that can be created
between the two sets. It is contemplated that in some aspects a
form of linking or concatenation can then be completed on the
tuples. For example, if one tuple created from two exemplary
two-dimensional geometries, such as ((1, 2), (5, 6)), includes two
ordered coordinate pairs, the tuple can be modified into (1, 2, 5,
6) which would be understood to be a geometric coordinate or data
point in a four-dimensional coordinate space.
[0048] It is also contemplate that on tuples of mesh element
points, degrees of freedom ("DOF") can also be defined for
dependent variables. Furthermore, in some aspects, shape functions
can be defined on each geometry where discretization is performed.
For each tuple, shape functions can form an expression that may be
product. It is then contemplated that the discretized system may be
solved on the product geometry between the base geometry and the
one or more extra geometries.
[0049] Methods and system for setting up and solving models, such
as multiphysics models based on coupled systems of PDEs, along with
other modeling systems are described in U.S. Pat. No. 8,219,373,
issued Jul. 10, 2012; U.S. Pat. No. 7,623,991, issued Nov. 24,
2009; U.S. Pat. No. 7,519,518, issued Apr. 14, 2009; U.S. Pat. No.
7,596,474, issued Sep. 29, 2009; and U.S. Patent Application
Publication No. 2012/0179426, published Jul. 12, 2012. Ser. No.
13/184,207, filed Jul. 15, 2011, each of which are hereby
incorporated by reference herein in their entireties. These
published patent documents describe, for example, method for
setting up and executing multiphysics simulations, including
several coupled physical phenomena, by receiving inputs in the form
of physical properties that may be expressed in terms of physical
quantities. In addition, the above-referenced U.S. patents and
patent application disclose methods for setting up problems using
physical properties, physical quantities, and physical phenomena
described using partial differential equations (PDEs). These
published patent documents provide for methods and systems for
setting up and solve multiphysics problems using predefined
application modes that are otherwise referred to in the present
descriptions as physics interfaces. Components of the physics
interfaces can include parameters, variables, physical properties,
physical quantities, boundary and initial conditions, and solvers
with settings and menus. These settings and menus may be tailored
for the specific physics instead of using the generic mathematical
settings. In addition, these published patent disclosures also
describe methods for PDE modes, also referred to as PDE interfaces,
in the cases where predefined physics interfaces are not available.
The use of the generic PDE modes and PDE interfaces for setting up
multiphysics problems requires knowledge about the description of
physical properties, physical quantities, and physical phenomena in
terms of PDEs.
[0050] It can further be desirable for modeling methods and system
to include processes for defining coupled systems of equations,
including coupled systems of differential equations and PDEs, on
product geometries. It is further desirable for modeling methods
and systems to include processes for solving coupled system of
equations on product geometries. It is yet further desirable for
modeling systems and methods to include processes for adding
additional or extra geometries as Cartesian products to a base
geometry of a model of a physical system.
[0051] In some aspects of the present disclosure, methods and
systems for forming different of product geometries (e.g., a
product geometry of all tuples, a product geometry expressed as
start and end conditions for creating tuples) are contemplated. In
some aspects, a user of the modeling system can extend a physics
interface to solve problems on product geometries of arbitrary
dimensionality. It is also contemplated that physics interfaces can
be provides that build models that are defined on product
geometries. For example, in the exemplary gas model discussed
above, a user of a modeling system could draw or provide the space
in which the gas is contained and the velocity distribution can be
predefined as a sphere. Then, in some aspects, a product geometry
between the user defined spatial space and the predefined sphere
can be formed automatically by the contemplated system and methods
of the present disclosure. It is further contemplated that
formation of a product geometry, such as in the example of the gas,
including determining the predefined sphere and the definition of
extra geometries can occur within the modeling system without being
displayed on a graphical user interface to the user of the modeling
system.
[0052] In some aspects of a modeling system, it can be desirable to
model thin structures using shells where physical propert(ies) are
described as function(s) of physical quantit(ies) along the
thickness of the shell. For example, in some aspects of the present
disclosure, a method for adding a thickness direction in the form
of an extra dimension is contemplated using an extra geometry that
is a line segment. The exemplary line segment can be divided into
several sub-line segments, and the sub-line segments can include or
be defined with different physical properties such as material
properties. This aspect can be particularly desirable because it
allows physical quantities such as displacements, stresses, and
strains to be modeled along the thickness of the shell. The
exemplary aspect of thin structure modeling by applying shells and
extra geometries is particularly desirable and provides certain
computational advantages. For example, shell problems such the one
described can also be solved by modeling the shell as a
three-dimensional solid. However, the meshing of a shell and adding
an extra geometry is a preferable and better way of defining a thin
structure than defining it as a full three-dimensional solid,
particularly where the dimensions of the structure are several
orders of magnitude larger than the thickness of the thin shell. An
example of such a thin shell structure may be an airplane
fuselage.
[0053] Other exemplary physics interfaces where it can be
beneficial to model the physical system using product geometries of
a base geometry and one or more extra geometries include beams,
reactors including porous particles, radiation in a participating
media, perfectly matched layers ("PMLs"), and others. For example,
for a beam, the data representing a beam cross section is defined
as an extra geometry and data representing the beam axis is defined
is a base geometry. For a reactor including porous particles, data
representing the particles defines an extra geometry and data
representing the bulk of the reactor represents the base geometry.
For radiation in a participating media, an extra geometry can model
the directional dependence and any wavelength dependence while the
base geometry provides a spatial distribution. For PMLs, data
representing boundaries is defined as a base geometry and data
representing the PMLs is defined as one or more extra geometries.
The PMLs are added to the boundaries by forming product geometry
data representing a product geometry between the base geometry and
the one or more extra geometries. It is further contemplated that
for the PMLs, a scaling operation can also be defined on the
product geometry.
[0054] It is contemplated that in some aspects equations,
variables, operators, materials, boundary conditions etc. can be
defined on a portion of a product geometry, which may also be
referred to as a product of selections. In some aspects, such
portions of a product geometry can be constructed, formed, or
computed as Cartesian products between some of the geometric
entities forming a product geometry in a base geometry, and some of
the geometric entities in extra dimensions forming a product
geometry. Some aspects of the present disclosure include a method
for making such selections by selecting base geometry entities and
extra geometry entities in a graphical user interface.
[0055] It is further contemplated that in some aspects various
properties can be defined on product geometries or parts thereof by
defining the desired properties on entities of an extra geometry.
The properties defined on the entities of the extra geometry can
then be applied to a Cartesian product of base geometry entities
and the extra geometry entities. For example, a thickness direction
of a multi-layer shell can be described or defined as an ordered
set of layers where each layer includes material properties and a
thickness. From such an ordered set of layers, a line segment can
be constructed or provided automatically with several sub-line
segments with each segment representing an extra geometry entity,
which can include material properties being defined upon it. The
line segment is the extra geometry of an extra dimension and can
automatically form a product geometry with user-defined or
pre-selected base geometry entities in the form of a shell. The
material properties and certain other properties defined on the
extra geometry entities can then applied to the portions of the
product geometry, of which the extra geometries entities are a part
of.
[0056] It is contemplated that the simulation methods for modifying
a geometry of a model of a physical system can be executed as a
standalone system that interfaces or connects with an engineering
analysis system, such as a multiphysics modeling system. It is also
contemplated that the simulation method for modifying a geometry
can be one of a plurality of modules or routines that comprise an
engineering analysis system. The simulation methods and systems can
include or be connected with a user interface, such as a graphical
user interface, that seeks inputs and displays instructions to a
user. The simulation methods for modifying a geometry of a model of
a physical system can be executed on one or more processors
associated with various computer systems described elsewhere herein
including, among other things, the computer systems and apparatus
described for the multiphysics modeling system.
[0057] It is contemplated that is would desirable for the
simulation method to be available in, or accessible to, an
engineering analysis system, such as a multiphysics modeling
system, as part of generating a model described in a model object
(e.g., a model data structure including data fields and methods
along with their interactions) in accordance with an
object-oriented programming language (e.g., C++, C#,
Java.RTM.).
[0058] In certain aspects of the present disclosure, a system or
simulation method for generating a modified geometry of a model of
a physical systems is contemplated that may be based, at least in
part, on PDE formulations. The modified geometry may be generated
using inputs received via a dedicated graphical user interface. The
modified geometry is contemplated to be useful for engineering
analysis processes operating on computer system(s) that include
modules or routines for performing finite element analysis methods,
finite volume methods, computational fluid dynamic methods,
multiphysics methods, and the like. Computer systems embodying the
engineering analysis processes may be configured with one or more
graphical user interfaces that allow a system user to input and
execute simulations. The computer systems may include some of the
non-limiting exemplary routines or methods described above and can
further include different interfaces for different types of
simulations. Different user interfaces may, for example, be
provided for fluid flow, heat transfer, electromagnetic, and/or
structural mechanics simulations. Simulations and associated
interfaces for other engineering or physics phenomena are also
contemplated for computer-aided engineering analysis systems.
[0059] Systems having a dedicated graphical user interface for
modifying a geometry of a model of a physical system are
contemplated in certain aspects of the present disclosure. For
example, a computer system may include a graphical user interface
for defining the parameters, variables, physical properties,
physical quantities, and/or physics interface features for a
desired physics phenomena associated with a desired analysis or
simulation. It is contemplated that the various routines or methods
associated with the system can be executed locally on, and/or
remotely through network connection(s) to, one or more processing
unit(s) executing engineering analysis or simulation systems.
[0060] One exemplary aspect of a an engineering analysis method
operating on a computer system that is contemplated by the present
disclosure includes routines for setting up and solving
multiphysics problems for simulations that may have several coupled
physical phenomena. Input(s) for the analysis method(s) can be
received in a form representative of physical properties that are
further expressed in terms including physical quantities. The
engineering analysis methods can also include routines for setting
up problems using physical properties, physical quantities, and
physical phenomena described using PDEs. It is contemplated that
the setting up and solving of a multiphysics problem using the
exemplary engineering analysis method can be accomplished via
predefined physics interfaces. In addition, the setting up and
solving of multiphysics problems may also be accomplished using PDE
interfaces, which may also be referred to as PDE modes in
situations where predefined physics interfaces are not available.
It is contemplated that the use of the generic PDE interfaces for
setting up a multiphysics problem can be accomplished by describing
the physical properties, physical quantities, and physical
phenomena in terms of PDEs.
[0061] Computer systems may be used for performing the different
tasks described in the present disclosure. One aspect for using a
computer system includes executing one or more computer programs,
including engineering analysis components and methods, stored on
computer readable media (e.g., temporary or fixed memory, magnetic
storage, optical storage, electronic storage, flash memory, other
storage media). A computer program may include instructions which,
when executed by a processor, perform one or more tasks. In certain
embodiments, a computer system executes machine instructions, as
may be generated, for example, in connection with translation of
source code to machine executable code, to perform modeling and
simulation, and/or problem solving tasks. One technique, which may
be used to model and simulate physical phenomena or physical
processes, is to represent various physical properties and
quantities, of the physical phenomena or physical processes being
modeled and simulated, in terms of variables and equations or in
other quantifiable forms that may be processed by a computer
system. In turn, these equations or other quantifiable forms may be
solved by a computer system configured to solve for one or more
variables associated with the equation, or the computer may be
configured to solve a problem using other received input
parameters.
[0062] It is contemplated that computer programs for modeling and
simulating physical phenomena or physical processes may provide
many advantages particularly as the complexity of the physical
phenomena or physical processes being modeled and simulated
increases. For example, in certain aspects a user can combine one
or more physical phenomena into a multiphysics model, as part of,
for example, an engineering analysis. To further illustrate this
example, a user may combine phenomena described by chemical
kinetics and fluid mechanics, electromagnetic phenomena and
structural mechanics, or other physics phenomena. Such multiphysics
models may also involve multiple physical processes. For example, a
process may be combined that includes an amplifier powering an
actuator, where both the amplifier and the actuator are a part of
one multiphysics model. Multiphysics modeling can also include
solving coupled systems of partial differential equations
(PDEs).
[0063] It may be desirable in certain aspects to model physical
quantities of coupled multiple processes using different sets of
PDEs, defined for different geometries and/or in different
coordinate systems, to represent the different coupled multiple
processes. It is contemplated that in certain embodiments, systems
of PDEs defined for multiple geometries can be desirable. PDEs can
provide an efficient and flexible arrangement for defining various
couplings between the PDEs within a single geometry, as well as,
between different geometries.
[0064] It is contemplated that computer systems on which
multiphysics modeling systems operate, such as the modeling systems
described herein, can include networked computers or processors. In
certain embodiments, processors may be operating directly on the
multiphysics modeling system user's computer, and in other
embodiments, a processor may be operating remotely. For example, a
user may provide various input parameters at one computer or
terminal located at a certain location. Those parameters may be
processed locally on the one computer or they may be transferred
over a local area network or a wide area network, to another
processor, located elsewhere on the network that is configured to
process the input parameters. The second processor may be
associated with a server connected to the Internet (or other
network) or the second processor can be several processors
connected to the Internet (or other network), each handling select
function(s) for developing and solving a problem on the
multiphysics modeling system. It is further contemplated that the
results of the processing by the one or more processors can then be
assembled at yet another server or processor. It is also
contemplated that the results may be assembled back at the terminal
or computer where the user is situated. The terminal or computer
where the user is situated can then display the solution of the
multiphysics modeling system to the user via a display (e.g., a
transient display) or in hard copy form (e.g., via a printer). It
is also contemplated that the solution may be stored in a memory
associated with the terminal or computer, or the solution may be
stored on another server that the user may access to obtain the
solution from the multiphysics modeling system.
[0065] Referring now to FIGS. 1A-1E, an exemplary flowchart and
wizard for the creation of a base model is illustrated according to
some aspects of the present disclosure. In FIG. 1A, an exemplary
flowchart is illustrated for a process for creating or forming a
base model. It is contemplated that a base model generally does not
include a base geometry until such base geometry is created,
imported, or retrieved. The steps in the flow chart may be
implemented, for example, in a multiphysics or other type of
physics simulation system. At least a portion of each of the steps
can be implemented in the form of graphical user interfaces
("GUIs") displayed by the system to the user of the modeling
system.
[0066] A base model is a model including one or more physics
interfaces. The exemplary system for creating the base model in
FIG. 1 includes options for selecting dimensions that include 0-D,
1-D, 1-D axisymmetric, 2-D, 2-D axisymmetric, or 3-D. The base
model can include geometries, also referred to as base geometries.
In some aspects, base geometr(ies) can be constructed or determined
from geometric primitives and operations, by importing a file or by
interfacing the modeling system with computer-aided design ("CAD")
system or by otherwise receiving or inputting the geometry into the
modeling system. The geometry can include a collection of geometric
entities and the entities can be connected manifolds, such as
volumes, surfaces, curves, or vertexes, that are also referred to
as points. A summary of exemplary modeling terms applied to some
geometric entities is included in FIG. 2 where a modeling term can
depend in some situations on the dimensions of the geometry.
[0067] Referring back to FIG. 1A, at step 101, the process for
creating the base model is commenced and this can be done via the
exemplary aspect illustrated in FIG. 1B of selecting the "New" icon
101a in dropdown menu presented in a GUI. Next, in step 102, the
dimension of a base model is specified or determined. One exemplary
aspect of specifying the dimension is illustrated in FIG. 1C where
a system user can select the base model dimension from a list of
options displayed in a GUI. In this example, a 3D icon or button
102a is selected, though any one of several options are available.
Next, at step 103, an exemplary interface with a menu of physics
interface options is displayed to a user, as illustrated in FIG.
1D. Selections of one or more physics interfaces can be received by
the modeling system and applied to the base model. For example, the
user can select from one or more physics interfaces included in a
physics interface lists 103a in a wizard. A desired physics
interface can then be added to a base model by selecting the
interface listing itself or a corresponding icon 103b. An added
physics interface can also be removed by selecting a previously
added physics interface and selecting a "remove" icon 103c. In the
exemplary aspect of FIG. 1D, the user has selected shell and beam
physics, though any of the listed physics or others can be
selected. As discussed here and elsewhere in this disclosure, it is
contemplated that the physics interfaces can include operations for
defining variables, parameters, expressions, initial values, shape
functions, solvers, and settings for a base model. For example, the
physics interfaces can include expressions in the form of user
editable partial differential equations (PDEs) expressing physical
quantities and physical properties. The variables, parameters,
expressions, initial values, shape functions, solvers, and settings
can further include identifiers that may be assigned automatically
and be unique to the particular modeling system. It is contemplated
that the variables, parameters, expressions, initial values, shape
functions, solvers, and settings can be accessible to and changed
by the user.
[0068] Next, at step 104, a selection can be received for a study
type to be implemented for a simulation including the base model.
For example, an exemplary study type list 104a can be displayed to
a user from which a study type can be selected, as illustrated in
FIG. 1E. A study type can define a sequence of study steps
including stationary, eigenvalue, eigenfrequency, or time dependent
study step sequences, along with others. In one exemplary aspect, a
study can include implementing a stationary study step that can
then be used to compute the initial conditions for a subsequent
time-dependents study step.
[0069] Finally, at step 105, the exemplary process of creating a
base model can be finalized by selecting a "Finish" icon 105a or
through some other trigger. A created or form base model can
include a set of predefined variables, parameters, physical
properties, physical quantities, boundary conditions, initial
conditions, and solvers that are determined according to user
selections in the previous steps of the base model creation
process. It is contemplated that a final base model can be
displayed and otherwise accessed via additional interfaces
displayed by the modeling system. To the extent a user would to
edit the base model, in some aspects it is contemplated that a user
may go back or proceed to the next step in the process by selecting
the "back" icon 103d or "forward" icon 103e or finish the process
by selecting the "finish" icon 105a. It is also contemplated that a
user can omit making selections in steps 103 and 104 by making
similar selections; in some aspects this can be done using the same
or similar icons (e.g., 103d, 103e, 105a). Furthermore, the process
can proceed immediately to step 105 at any time by selecting the
"finish" icon 105a, bypassing any intermediate steps.
[0070] Referring now to FIGS. 3A-3B, exemplary GUIs 310, 320 with
menus are illustrated for adding a physics interface and study to a
base model, according to some aspects of the present disclosure. In
some aspects, if the user omitted to make selections of physics
interfaces or study type in method steps 103 or 104, or wants to
make additional choices, the user may add additional physics
interfaces or study types to a base model. The user may do so by
selecting the base model node 300a and further selecting an "add
physics" icon 300b from a subsequent menu. The process can then
proceed to the exemplary physics interface list 103a in FIG. 1D.
Similarly, a user may add a study by selecting a root node 300c in
FIG. 3B from a the model builder window and further selecting an
"add study" icon 300d, also from a subsequent menu, and then the
process can proceed to the exemplary study list 104a in FIG.
1E.
[0071] Referring now to FIGS. 4A-4C, an exemplary flowchart and
wizard for adding one or more extra dimension to a base model is
illustrated, according to some aspects of the present disclosure.
It is contemplated that extra dimensions may be added as child
features to a base model. The child features can be described in
0-D, 1-D, 1-D axisymmetric, 2-D, 2-D axisymmetric or 3-D. It is
contemplated that an extra dimension feature can further include an
extra geometry, where settings for physical quantities and physical
properties can be defined.
[0072] In some aspects of the disclosed simulation systems and
methods for modifying a base geometry or otherwise adding extra
dimensions, physics interfaces of a modeling system can include
instructions or operations for automatically defining extra
dimension features. For example, the modeling system can include
predefined variables, parameters, physical properties, physical
quantities, boundary conditions, and initial conditions for a set
of extra dimensions. Solvers may also be adapted or configured for
solving models that include base geometries or base model with
extra dimensions added thereto.
[0073] In some aspects of a modeling system, extra dimension
features can be added manually to a base model, such as where an
extra dimension feature is not predefined in a physics interface.
In these situations, variables, parameters, physical properties,
physical quantities, boundary conditions, initial conditions, and
solvers are defined manually in the extra dimensions.
[0074] In FIG. 4A, steps 401 through 405 are similar to the process
described in FIGS. 1A-1E for forming or creating a base model that
includes a base geometry. Then, at step 406, an extra dimension
feature is added to the base model. In one exemplary aspect of step
406, GUI(s) such as the one(s) illustrated in FIGS. 4B and 4C are
displayed to a user of the modeling system that allow selection(s)
to be received first of the base model node 406a and then of an
"Add extra dimensions" icon 406b that may be displayed in a context
menu or otherwise. The user can then be provided the option to
select a button 406c or icon associated with the dimension (e.g.,
1-D, 1-D axisymmetric, 2-D, 2-D axisymmetric, 3-D) of the extra
dimensions feature. The selection can be made, for example, via a
dimension list in a separate window or via the wizard previously
described in FIGS. 1A-1E.
[0075] It is contemplated that a physics interface in the modeling
system can be configured to automatically define settings for the
one or more extra dimensions following a user's selection or
activation of extra dimensions. In certain aspects, it is also
contemplated that a physics interface can be predefined to include
extra dimensions by default. The below discussion includes some
examples of situations where extra dimensions can be automatically
generated.
[0076] In some aspects, a GUI can be presented to a user that
receives selections for implementing a process to automatically add
perfectly matched layers to a base geometry. The process can
further automatically define the PMLs following the receipt of a
user's selection to add PMLs to a domain.
[0077] In some aspects, a GUI can be displayed to a user for
selecting a shell physics interface. It is contemplated that the
shell physics interface can be configured to generate a predefined
extra dimensions feature for describing certain physical quantities
and physical properties along the thickness of a shell. Such an
extra dimension feature can, for example, be added by a modeling
system user to allow for some customization of a model, or the
extra dimension feature can be included by default for certain
shell interfaces. For example, shell interfaces for thick or
nonlinear shells may by default include a 1-D extra dimensions
feature for describing physical properties as functions of physical
quantities along the thickness of the shell.
[0078] In some aspects, a GUI can be displayed to a user for
selecting a beam physics interface that includes extra dimension
features for describing or defining a cross section of a beam. It
is contemplated that the extra dimension features can be activated
by the user based on selection, for example, for manually defining
cross section(s), or the extra dimension features can be included
based on defaults for certain predefined cross sections. For
example, an H-beam interface may by default include a 2-D extra
dimensions feature that includes a description of the H-cross
section of the beam.
[0079] It is also contemplated that in some aspects a GUI can be
displayed to a user for selecting a physics interface for modeling
reactors with porous particles. The interface can include, for
example, a predefined 1-D extra dimensions feature for describing
transport and reactions along the radius of the particles. The
extra dimension feature can be activated by a user or it may be
included by default in the physics interface. For example, a
physics interface for lithium-ion battery modeling can by default
include a predefined 1-D extra dimension feature for describing
lithium intercalation in graphite particles.
[0080] In some aspects, a GUI can be displayed for selecting a
physics interface for modeling heat transfer that includes an extra
dimension feature for describing radiation along an independent
variable for wavelength. It is contemplated that while an extra
dimension in this exemplary aspect may not have a geometric
physical meaning it is a useful alternative for modeling heat
transfer and radiation effects. Similarly, an extra dimension can
be applied in another exemplary aspect to model along a coordinate
that represents energy in the Boltzmann equation.
[0081] The process of adding selected extra dimensions to a base
model, as exemplified above and in the context of the exemplary
aspects described herein, can be finalized at step 407 by a user
selecting a "finish" icon 407a in the GUI exemplified in FIG.
4C.
[0082] Referring now to FIGS. 5A-5C, exemplary menus are
illustrated including extra dimension features that are added as a
child feature to a base model, according to some aspects of the
present disclosure. As discussed elsewhere, one or more extra
dimension features can be attached to a base model. An extra
dimension node 500 can include one or more child nodes for defining
an extra dimension.
[0083] In some aspects, a definitions child node 500a includes
another child node 500b that is further denoted by "Points to
Attach" in the tree illustrated in FIGS. 5A and 5B. The child node
500b can be used to identify one or more vertices in an extra
geometry that are connected to entities in a base geometry in the
base model. This may assist in identifying physical quantities and
physical properties in a product geometry with the corresponding
physical quantities and physical properties in a base geometry. For
instance, in an exemplary aspect of a base geometry including a 2-D
geometry forming a 3-D product geometry with a 1-D extra geometry
in an extra dimensions feature, the point of attachment can be used
identify a vertex in the product geometry which shares the value of
physical quantities and physical properties with the base
geometry.
[0084] A definitions context menu may be displayed by selecting the
definitions node 500a and include different settings 500c for view,
selections, extra dimension integration, variables, and coordinate
system. Additional child nodes may be added to the definitions node
by selecting one or more of the settings 500c. It is contemplated
that a user can define viewing setting such as light settings,
grids and geometry labels using additional settings available under
the "View" setting. Selections can be applied to create specific
selections of geometric entities, which may be customized by a
user. Extra dimension integration can be used to integrate over
geometries including extra dimensions. Variables can include
symbolic expressions that may be defined on the extra dimension,
though variables defined on a product geometry may be defined using
a variables node in the base geometry. Coordinate systems listed in
the context menu can include settings describing the coordinate
system of the extra dimension.
[0085] In some aspects, a geometry child node 500d can include
information about extra geometries created in an extra dimensions
feature. Furthermore, a mesh child node 500e can include
information about meshes on extra geometries. FIG. 5C illustrates
an exemplary settings window 500f for the extra dimension feature,
which can be accessed through user selections, such as a "Settings"
icon 500g. A settings window 500f can include a user editable extra
dimension identifier 500h which can be automatically set by the
system to a unique identifier. Furthermore, a settings window 500f
can also include user editable names 500i of spatial coordinates
that are applied in the extra dimension, where the unique names may
be automatically assigned by the system. It is also contemplated
that a geometry shape order 500j can be selected or set to an
automatic setting in the settings window 500f. The geometry shape
order sets the order of curved mesh elements that may be used to
describe an extra geometry using finite elements.
[0086] Referring now to FIGS. 6A-6B, exemplary menus, tools, and
graphical representations are illustrated for creating extra
geometries, according to some aspects of the present disclosure. A
GUI 600 is illustrated in FIG. 6A that can, for example, be
accessed or displayed in response to a user selecting the geometry
child node 500d from FIG. 5A. As a preliminary matter, a base
geometry can be created or can be otherwise available in a geometry
node 610. Selecting the geometry node 610 can confirm the presence
of a predetermined base geometry or allow the creation of the base
geometry. The base geometry can be created similar to the creation
of extra geometries, which are now described. An extra geometry can
be constructed from geometric primitives 600a and operations 600b,
exemplary aspects of which are included in FIG. 6A. The available
geometry primitives may be dependent on the dimension of the extra
dimensions feature. The geometric primitives and operations can be
child nodes of the geometry node(s). A user can define the
geometric primitives by selecting them, which may open a separate
settings window 600c, such as the exemplary window illustrated in
FIG. 6B, that allow for data to be received via specific fields
displayed in the settings window, and in some aspects, be displayed
graphically (see exemplary element 6000. It is also contemplated
that in some aspects, the base geometry and extra geometry data can
be imported 600d or received as file data stored in a memory device
or by linking 600e to a CAD system.
[0087] As previously described above, in some aspects where a
physics interface automatically defines extra dimensions features,
the shape of an extra geometry may be predefined. For example, when
adding a PML feature to a radio frequency model, adding a thickness
to a shell in a shell model, or adding a porous particle catalytic
bed to a reacting flow model, extra geometries in the form of line
segments can be generated automatically by the respective physics
interfaces. Some further examples include physics interfaces for
modeling heat transfer by radiation in 3-D, or Boltzmann equations
in 3-D, that generate spheres or surfaces of spheres as extra
geometries. For some aspects, a user can also define some
characteristics of the predefined shapes in a GUI, such as the
thickness of a shell in the shell model example.
[0088] It is contemplated that base dimensions and extra dimensions
include identifiers. In addition, geometries and geometric entities
also include identifiers. Such identifiers can be used to make
lists, code, and data-structures specifying sets of base geometry
entities that may form a Cartesian product with sets of such
identifiers of geometric entities in extra geometries. Such
Cartesian products are product geometries for non-discretized
geometries. Product geometries for non-discretized geometries can
be used to form or construct Cartesian products of discretized
geometries. For discretized base geometries and discretized extra
geometries, a product geometry is the Cartesian product of the set
of mesh element points of a selection of base geometry entities
with the mesh element points of an extra geometry or with a
Cartesian product of the sets of mesh element points of two or more
extra geometries.
[0089] Referring now to FIGS. 7 and 8A-8D, an exemplary flowchart
for creating a product geometry is illustrated along with exemplary
menus, tools, and graphical representations for selections of base
geometry entities and extra geometries are illustrated, according
to some aspects of the present disclosure.
[0090] In some aspects the process is initiated at step 701 by
selecting an option to attach extra dimensions, such as icon 800a
illustrated in FIG. 8A. At step 702, a selection or determination
of base geometry entities is made. This step can be implemented
through a first selection of a geometry entity level, through for
example a displayed list of options 800b (e.g., domain, boundary,
edge, point) or selectable icons 800c, as illustrated in FIGS. 8B
and 8C. Then, base geometry entities of the selected geometric
entity level can be displayed in a list 800d or can be displayed as
a graphical representation of a base geometry entity. It is
contemplated that in some aspects while only base geometry entities
of the selected geometry entity level may be displayed in step 702,
all base geometry entities directly adjacent to the selected
entities in the geometry, which are of a lower geometric entity
level, can further be automatically selected by the modeling
system. For example, in some aspects, for a 3-D geometry, if
"domains" is the displayed geometry entity level, and a domain is
chosen, all boundaries, edges, and vertexes directly adjacent to
the domain are also selected. As another example, for some aspects,
if a displayed geometry entity level is "edges" and an edge is
selected, only the two entity levels that are the directly adjacent
vertexes are automatically selected in addition to the selected
edge.
[0091] Next, at step 703, a selection of extra geometries is
implemented. In some aspects, this step can be implemented by
selecting one or more extra dimensions from a list 800f, such as
the one illustrated in FIG. 8D, or from graphical representations
of extra geometries, such as exemplary graphical representation in
element 800e in FIG. 8C or the graphical representation in element
600f illustrated previously in FIG. 6B.
[0092] Next at step 704, a determination is made if two or more
extra dimensions have been selected in step 703. If the
determination is true, a Cartesian product of the two or more extra
geometries is automatically constructed or computed in step 705.
The Cartesian product of extra geometries can also be referred to
as a product of extra geometries. If the determination is false,
only one extra dimension has been selected and the method proceeds
to step 706.
[0093] Next, at step 706, a product geometry is formed or computed
as a Cartesian product of the selection made in the step 702 with
the selection made in step 703 or with the Cartesian product formed
in step 705. In some aspects, the product geometry can be formed by
coupling a list, including pointers (or identifiers) to base
geometry entities selected in step 702, to a second list, including
pointers to the selection of extra geometries made in the third
method step 703.
[0094] Finally, at step 707, the process for creating a product
geometry is completed, and the product geometry from step 706 can
be stored or added to a list, code, or data structure.
[0095] It is contemplated that in some aspects if extra dimensions
features have been generated automatically by a physics interface
and extra geometries have been generated, instructions for the
process of forming product geometries are predefined. For example,
a product geometry between a 3-D geometry describing a shell and a
1-D geometry (e.g., a line) describing a thickness direction can be
formed automatically.
[0096] In some aspects, it can be desirable to define variables,
expressions, operations, and materials on at least a portion of a
product geometry. The portions of a product geometry can be
referred to as a products of selections. A product of selections is
conceptually similar to a product geometry, but there are some
differences. A product geometry is formed as a product of geometric
entities in a base geometry and geometric entities in extra
geometries. A product of selections differs in that it is a
Cartesian product of a selected portion of the geometric entities
of the base geometry and selected portions of the geometric
entities of the extra geometries. A portion of a product geometry
formed by a Cartesian product between a set of base geometry
entities and a set of extra geometry entities can also be referred
to as a product of entities. It is contemplated that a modeling
system can be operable to include a process or instructions for
creating a product of selections in various physics interfaces and
features. It is also contemplated that a product of selection tool
can be a feature itself in a physics or multiphysics simulation
system.
[0097] Referring now to FIGS. 9 and 10A-10E, an exemplary a
flowchart for creating a product of selections along with exemplary
menus and graphical representations for the product of selections
tool are illustrated, according to some aspects of the present
disclosure.
[0098] At step 901, it is contemplated that base geometry entities
are displayed, such as in a list 1000a as illustrated in FIG. 10A
or as a graphical representation of the base geometry, as
illustrated by elements 1000e and 1000f in FIGS. 10D and 10E. In
some aspects, the geometry entity level of the displayed base
geometry entities can be selected, and the base geometry entities
forming a product geometry can further be highlighted to a user,
for instance using a bolder font or a different color.
[0099] At step 902, a selection is made from among one or more base
geometry entities displayed in the list or in the graphical
representations displayed in step 901. Next, at step 903, the extra
geometries forming a product geometry with geometric entities in
the base geometry are displayed. In some aspects of the present
disclosure, the extra geometries can be displayed in a list 1000b,
as illustrated for example in FIG. 10A, along with the products of
extra geometries that are also displayed as list items. In some
aspects, it is contemplated the extra geometries can also be
displayed in graphical representations (e.g., cylinder at 1000e,
sphere at 1000f).
[0100] Next, at step 904, a selection is made from among the extra
geometries displayed in step 903. In some aspects, this selection
is made via exemplary selections made from a displayed or a
graphical representations displayed in a GUI. (see, for example,
elements 1000b, 1000e, 1000f in FIGS. 10A, 10D, and 10E). It is
contemplated that in some aspects of the process, if a selection of
extra geometries is made, such that the Cartesian product between
the base geometry entities selected in step 902 and the selected
extra geometries includes a product of entities that is not a
portion of the product geometry, any base geometry entity that is
part of such a product of entities will be automatically removed
from the selection in the second method step 902. It is also
contemplated in some aspects that the generation of such product
entities can generate an error message. In addition, it is
contemplated in certain aspects, to only allow selections of extra
geometries whose Cartesian product with the selection in step 902
forms at least a portion of the product geometry. It is further
contemplated that in some aspect such geometric entities are
highlighted (e.g., bolded font, different color), such as on a
display so as to be readily visible to a user of the modeling
system.
[0101] Next, at step 905, extra geometry sections are generated.
For example, in the GUI displayed in FIG. 10A, extra geometry
sections (e.g., 1000i) are automatically generated and appended to
the GUI based on the extra geometries selected in step 904. In the
exemplary sections 1000i in FIG. 10A, one section is generated for
each extra geometry from the selections made in method step 904.
For example, if a selection was made in the step 904 of a Cartesian
product between two extra geometries, two sections, one for each
extra geometry, can be generated. If a single extra geometry was
selected in step 904, then in some aspects only one section is
generated.
[0102] It is contemplated that in some aspects of the process for
creating or forming a product of selections, step 905 can include a
choice of geometric entity levels that can include several choices,
such as an entire (extra) geometry, domains, boundaries, edges, and
points. An exemplary aspect of an interface for receiving
selections of these choices or options 1000c is illustrated in FIG.
10B. Furthermore, for at least some of the geometric entity level
selections, a second set of selection options can be displayed to a
user in step 906. The options can include a "manual" option and
another option for (all) domains, (all) boundaries, (all) edges, or
(all) points in accordance with the option selected for the
geometric entity level. If "manual" is chosen, selection can be
received for geometric entity numbers displayed on a list of
entities or from a graphical representation thereof (which in some
aspects, may be displayed in step 906). An exemplary aspect of an
interface for receiving selections of these choices or options
1000d, 1000g is illustrated in FIG. 10C. In addition to being
displayed as lists of geometric entity numbers or options, such as
entire geometry, all domains, all boundaries etc., in step 906, the
extra dimension geometric entities may be displayed in a GUI. For
example, in exemplary FIG. 10D, one single boundary entity has been
shaded for clarity, while three adjacent boundaries are not, to
identify the extra dimension geometric entit(ies).
[0103] Next, at step 907, extra geometry entities, which may have
been displayed in step 906, can be selected using the sections
generated in step 905. In some aspects, a user can choose an entire
(extra) geometry, as illustrated in FIG. 10B, which would select
all domains, boundaries, edges, and points in the context of an
exemplary 3-D geometry. For other exemplary geometries, FIG. 2
provides indications of the extent of a result of a select all
choice. It is contemplated that in some aspects if a user instead
chooses domain, boundary, edge, or point from menu 1000c, a second
choice may be made from a second drop down list 1000d and the user
can select all geometric entities of a specific geometric entity
level or a manual option. If a user chooses the manual option, a
third choice can be made in another list 1000g or in a graphical
representation of the extra geometry, where specific geometric
entities can be selected. It is contemplated that the selection
process of step 907 is performed for each section generated in step
905. It is further contemplated that a set of geometric entities is
further be selected for each section.
[0104] Next, at step 908, a product of selections is formed. In
some aspects, the product of selections is formed as a Cartesian
product between the set of geometric entities selected from the
base geometry in the step 902 and the set of extra geometry
entities in step 907. It is contemplated that the product of
selections can be formed from a list including pointers (or
identifiers) to base geometry entities selected in step 902 and
then coupled using a second list including pointers to the
selection of extra geometry entities made in step 907.
[0105] As discussed above, it is contemplated that is can be
desirable to define variables, operations, expressions, and
materials on products of selections. These processes are described
in more detail below. Defining variables, operations, expressions,
and materials on a product of selections can involve including a
list defining a product of selections, or a pointer to such a list,
in a data structure describing variables, operations, expressions,
and materials.
[0106] Referring now to FIG. 11, an exemplary settings window for
defining variables on a product of selections is illustrated,
according to some aspects of the present disclosure. In some
aspects, a settings window can be accessed by selecting a
definitions node of a base model including a base geometry, forming
a product geometry with one or more extra geometries, and selecting
variables. Other aspects for accessing a setting window are also
contemplated. In some aspects, a variable can be defined by
entering a name (e.g., 1100a) for the variable and an expression
(e.g., 1100b). A product of selections can then be constructed or
formed using a product of selections tool exemplified by interface
1100c. An outcome of the formation of the product of selections can
include that a variable with the variable name (e.g., 1100a) and
the expression (e.g., 1100b) is then automatically defined on the
product of selections. Variables can also be defined on extra
geometries in a similar fashion by selecting variables in a
definitions context menu under an extra dimension feature (e.g.,
500a in FIG. 5A). In some aspects, it is contemplated that variable
can be defined on an extra geometry without being defined on a
product geometry or a product of selections including base geometry
entities. In such cases a variable may be assigned using a
variable's child node under the extra dimension node including such
an extra geometry.
[0107] Referring now to FIGS. 12A-12B, exemplary menus and a
settings window for defining an operation on a product of
selections are illustrated, according to some aspects of the
present disclosure. In some aspects, such as the exemplary settings
window and menus of FIGS. 12A-12B, an integration operation is
defined on a product of selection. It is contemplated that other
operations can be similarly defined, such as for minimum, maximum,
and average operations. In some aspects, a settings window can be
accessed by selecting a definitions node under a base model and
selecting model couplings, and integration (e.g., 1200a), as
exemplified by FIG. 12A. It is contemplated that an operation name,
such as the integration name, can be defined by a user (e.g.,
intop1 at element 1200b) or be automatically generated by a
multiphysics system. The integration on a product of selections can
be defined by using a product of selections tool or interface
exemplified thereby (e.g., 1200c). It is further contemplated that
the operation name (e.g., integration) can be used in other
features such as variables. For instance intop1(u) is the integral
over the variable, u, on the product of selection defined using a
product of selections tool.
[0108] It is further contemplated that in some aspect, a user can
integrate in extra geometries. For example, a user can select extra
dimension integration from a definitions context menu of an extra
dimensions feature. The user can then define an integration
operator with a name. The user may define the integration operator
on one or more extra geometries or parts thereof by selecting
geometric entities in a list or graphical representation of one or
more extra geometries. It is also contemplated that the user can
define an integration order of the integration operator. One or
more such integration operators may be used to form expressions. An
example of such an expression is xd3.intop2(u), which may be used
to integrate over the variable, u, over some part of extra
geometries in extra dimension 3, xd3. intop2 is the name of the
integration operator, xd3 signifies that intop2 is the name as
defined in extra dimension 3. xd3 may not be necessary if the name
intop2 is unique. u may denote a variable representing a physical
quantity.
[0109] To integrate over a product of extra geometries using
strings, it is contemplated that two or more integration operators
are used. An example of such an expression is:
xd2.intop1(xd3.intop2(u)). Here xd2.intop1 refers to integration in
extra geometries or parts thereof in extra dimension 2 and
xd.3intop2 refer to integration in extra geometries or parts
thereof in extra dimension 3 and u is a variable.
[0110] It is contemplated that other operators for finding the
average, maximum, or minimum value of a variable may work in a
similar fashion using operator names such as avg1, max1 or
min1.
[0111] Operators for pointwise evaluation of variables are also
contemplated in some aspects. These operators can be used in
strings in a similar fashion to what is described above with the
additional specification of the dimensionality of the entity in
which to evaluate. For example, to evaluate the variable u on a
boundary (1-D) of a 2-D extra geometry in an extra dimension with
an identifier xd3 and global coordinates (0.3, 0.4), the following
exemplary string may be used: xd3.atxd1(0.3,0.4,u). Here, xd3
specifies that the operation on u is with respect to the variable
named u in xd3. atxd is the name of the operator which evaluates a
variable in a point. atxd1 specifies that the evaluation is on a
1-D extra geometric entity (hence the 1 after atxd). 0.3,0.4 gives
the coordinate pair and, u, the variable to be evaluated.
[0112] In some aspects, to make a pointwise evaluation in a product
of extra geometries, more than one atxd operator is used. For
example, given the product of extra geometries between a 1-D extra
geometry in an extra dimensions xd4 and a 2-D extra geometry xd2,
the following string may be used to find the value of u (in the
point (0.7,0.9) in xd4 and the point (0.5) in xd2) on the product
of entities formed between the boundary of xd2 and the xd4 domain:
xd2. atxd1(0.7,0.9,xd4.atxd1(0.5,u)).
[0113] Referring now to FIG. 13A-13C, exemplary menus and a
settings window for defining material properties on a product of
selections are illustrated, according to some aspects of the
present disclosure. In some aspects, a settings window (e.g.,
1300a) can be accessed by selecting a materials node (1300b) and
further selecting material (e.g., 1300c). Once in the settings
window, a user can define various material properties (e.g.,
1300d). A product of selections can be constructed using a product
of selections tool as exemplified by interface 1300e. The material
properties set in the interface (e.g., 1300d) can automatically be
defined on the product of selections. Alternatively, it is also
contemplated that a predefined material can be used on a product of
selections by accessing a material browser, selecting a predefined
material, selecting the node for the predefined material, accessing
a settings window including a product of selections tool, and then
defining a material on a product of selections. A selected material
can include an identifier, which may be used when defining
materials on products of selections in other ways, such other ways
are described elsewhere.
[0114] It is also contemplated that in some aspects materials and
other properties can be defined using a specific tool for defining
a material and other properties on geometric entities in extra
geometries. For example, when forming products of entities with
entities in base geometries, the material and other properties
defined on the entities in the extra geometries may be
automatically defined on the product of entities. Several such
tools may be combined in one feature, where each tool is located in
a part of a settings window of the feature. It is also possible
that the tools may be separate features. Such tools may be referred
to as "materials sections tools".
[0115] Referring now to FIGS. 14A-14B, exemplary materials settings
windows are illustrated for defining properties on a geometry that
may be an extra geometry forming a product geometry, according to
some aspects of the present disclosure. It is contemplated that
such a settings window can include different parts for different
kinds of materials sections. Examples of such parts include layered
structures, pipes, beam cross sections, and inhomogeneous
materials.
[0116] It is contemplated that layered structures can be used for
examples describing multi-layer shells. A multi-layered shell can
include several layers in a specific order. Each layer may have
certain properties such as material, layer thickness, and in some
instance layer orientation. Each layer can be identified by one or
more identifiers. Several such layers can form a layer section that
may be identified by a user editable identifier. The layered
structures materials section can include user editable fields and
drop down lists. Exemplary aspects of such fields from FIG. 14A
include number of layers 1400a, layers section identifier 1400b,
layer order 1400c, layer thickness 1400d, layer material 1400e,
layer orientation 1400f, and layer identifiers 1400g.
[0117] It is contemplated that in some aspects the number of layers
field a user can define the number of layers that are in a layer
section. The number affects the number of fields and drop down list
that can be made available. For instance if 3 is typed in the
number of layers field the system may automatically create 3 sets
of fields and drop down list, each set of fields and drop down
lists describing one layer.
[0118] It is contemplated that in some aspects the layers section
identifier can include a user editable identifier for a set of
layers.
[0119] It is contemplated that in some aspects the layer order can
describe the position of an individual layer among other layers.
Such a position may be described by a number, for instance 1,
designating a lowest layer, and 2, the layer above the lowest layer
etc.
[0120] It is contemplated that in some aspects layer thickness can
describe the thickness of an individual layer. This may be
described as a fraction of a total thickness of all layers, as a
physical quantity, or as an expression of physical quantities.
[0121] It is contemplated that in some aspects layer material can
include a user editable field where a user may identify a material
by its unique identifier. It is also contemplated that a user may
identify a material in some other way or there may be several sub
fields where a user could designate one or more material
properties.
[0122] It is contemplated that in some aspects layer orientation
can include a list with selections such as isotropic, or
anisotropic, where a section in a settings window may allow the
definition of the orientation of the layer in relation to a
coordinate system.
[0123] It is contemplated that in some aspects layer identifiers
may include the name of a layer or descriptors. A user may add more
identifiers as needed. Layer identifiers may be used elsewhere in
the software to refer to all layers including such identifiers.
[0124] In some aspects, a layered structures materials section can
includes a layer number menu where a user can select a layer, as
exemplified by element 1400j in FIG. 14B. An example of such a
layered structures materials section is exemplified by element
1400i. In another part of the layered structures materials section,
layer thickness, layer material, layer orientation, and layer
identifiers can be specified for the selected layer. In this
example, the user defines the layer in a certain position rather
than defining layers and their position.
[0125] It is further contemplated that an extra geometry can be
automatically constructed or formed using information received from
the described fields. For example, a line segment can be
constructed, where the line segment is divided into several
sub-line segments, and each sub-line segment having a length
defined by the layer thickness field. The order of the line
segments can be defined by the layer order fields and the
material.
[0126] In some aspects, it is contemplated that an exemplary pipe
materials section can include user editable fields and lists.
Examples of such fields and lists include pipe shape, surface
roughness, layers, and pipe identifiers. Pipe shape can describe
the cross section of the pipe. The cross-sections can include
predefined shapes such as circular with a user defined radius,
square or rectangular with user defined sides, other
two-dimensional shapes that may be defined by a set of parameters,
user defined cross section with a user defined cross sectional area
and wetted perimeter, or a user defined cross-section which may be
imported or constructed using geometry tools in a multiphysics
modeling system. A drop down list may include the possibility to
describe surface roughness of pipes using several common roughness
parameters, or the roughness may be defined as a physical
quantity.
[0127] It is contemplated that layers can be described by lists and
user editable fields such as those described for layered
structures. It is also possible that a layer can be referred to by
an identifier. Pipe identifiers can include the name of a pipe
material section or descriptors. A user may add more identifiers if
needed. Pipe identifiers may be used elsewhere in the system to
refer to all pipes including such identifiers.
[0128] In some aspects, beam cross sections are contemplated that
can include fields such as cross-sectional area, moment of inertia
about local z-axis, distance to shear center in local z direction,
moment of inertia about local y-axis, distance to shear center in
local y direction, or torsional constant. Bending stress evaluation
points can be chosen, for example, from section heights or from
specified points using list that depend on which one of the
following two sets of fields that may be present. If based on
section heights, the list can include, section height in local
y-direction, section height in local z direction, torsional section
modulus, max shear stress factor in local y direction, and max
shear stress in local z direction. If based on specific points, the
list can include list of points in cross section, torsional section
modulus, max shear stress factor in local y direction, and max
shear stress factor in local z direction.
[0129] In some aspects, a materials section tool for inhomogeneous
materials is contemplated that can include edit fields and lists.
Examples of such edit fields and lists include fractions and
material for each fraction. The materials section tool can include
operations for saving materials sections to a file in a memory or
loading materials sections from a file to a memory accessible to
the modeling system.
[0130] Referring now to FIGS. 15A-15C, exemplary menus and a
settings window for adding weak contributions to a product of
selections is illustrated, according to some aspects of the present
disclosure. In some aspects, a user can add a weak contribution to
a portion of a product geometry using the product of selections
tool (see, e.g., FIG. 9). If the user specifies the weak
contribution as a weak equation and also defines and uses an
auxiliary dependent variable (shown elsewhere), such a dependent
variable can then be created on a product of selections. The
ability to define weak contributions (or weak constraints, or
point-wise constraints or auxiliary dependent variables) on product
geometries can be a desirable operation that offers computational
advantages. The exemplary settings windows illustrated in FIG. 15A
can be accessed by selecting a physics interface node. In some
aspects, as illustrated in FIG. 15C, further selections are
contemplated including an option for selecting "more", "edges",
"point", or "global" options and selecting an add weak contribution
option 1500b. In addition, it is contemplated that in some aspects
an advanced physics option 1500c is selected, as illustrated in
FIG. 15B. The settings window exemplifies a product of selections
interface 1500d associated with a product of selections tool (see,
e.g., FIG. 9) which may be used to define a weak expression entered
in a weak expressions field 1500a on a product of selections.
[0131] Referring now to FIGS. 16A-16B, exemplary menus and a
settings window for adding a weak constraint to a product of
selections are illustrated, according to some aspects of the
present disclosure. The settings window exemplified by FIGS.
16A-16B can be accessed by selecting a physics interface node. In
some aspects, further selections from a menu include selecting
"more", "edges" or "point" and selecting add weak constraint 1600a,
which can then open a settings window. The settings window
exemplified in FIG. 16B includes a product of selections interface
1600b associated with a product of selections tool for defining a
weak constraint entered in the constraint field 1600c on a product
of selections.
[0132] Referring now to FIGS. 17A-17B, exemplary menus and a
settings window for adding a point-wise constraint to a product of
selections is illustrated, according to some aspects of the present
disclosure. The settings window exemplified by FIGS. 17A-17B can be
accessed by selecting a physics interface node. In some aspects,
further selections from a menu include selecting "more", "edges" or
"point" and selecting add pointwise constraint 1700a, which can
then open a settings window. The settings window exemplified in
FIG. 17B includes a product of selections interface 1700b
associated with a product of selections tool for defining a
pointwise constraint entered in the constraint field 1700c on a
product of selections.
[0133] Referring now to FIGS. 18A-18B, exemplary menus and a
settings window for adding an auxiliary dependent variable to a
product of selections is illustrated, according to some aspects of
the present disclosure. An auxiliary dependent variable may be
added by selecting an auxiliary dependent variable node 1800a.
Adding an auxiliary dependent variable as well as a weak equation
can be desirable for allowing a user to define weak equations on a
product of selections. The field variable name 1800b can be the
name of the dependent variable. An initial value and an initial
time derivative may also be set, as exemplified in FIG. 18B. A user
may also use a product of selections interface 1800c associated
with a product of selections tool (see, e.g., FIG. 9) to define the
auxiliary dependent variable on at least a portion of the product
selections on which the weak contribution is defined. Typically,
the portion can include all the product of selections on which the
weak contribution is defined. In some aspects, a product of
selections tool of the auxiliary dependent variable may not define
an auxiliary dependent variable outside of the product of
selections on which the weak contribution is defined. In addition,
a user may define the shape function type and element order used
when the auxiliary dependent variable is discretized.
[0134] It is contemplated that in some aspects of the simulations
methods and systems described herein that initial values on
products of selections described, for example, in FIG. 9 and
thereafter, are set and that the setting of the initial values is
implemented through physics interfaces, such as those of a
multiphysics modeling system.
[0135] It is further contemplated that PDEs can be applied to form
a system of user editable coupled PDEs, whether the PDEs are
predefined on product geometries by physics interfaces or by a
user. To solve the system of coupled PDEs, the PDEs can be
discretized and DOFs defined on discretized product geometries. To
determine the number and locations of DOFs, the base geometry and
extra geometries are meshed, discretizing the base geometry and the
extra geometries in mesh elements expressed by shape functions. A
discretized product geometry is formed by the set of mesh points on
the base geometry and the set of mesh points on extra geometries
forming a Cartesian product. Such a Cartesian product includes
tuples of mesh points on which the DOFs are defined. Once the base
geometry and the extra geometries have been meshed, a product
geometry has been formed, and DOFs have been assigned, then the
model may be solved.
[0136] Referring now to FIG. 19, exemplary menus and a settings
window for defining a mesh on a product of selections is
illustrated, according to some aspects of the present disclosure.
The mesh settings window for the base geometry and the extra
geometries can be accessed by selecting mesh options 1900a (e.g.
Mesh1, Mesh2 respectively) under the base model and under the extra
dimensions, as exemplified in FIG. 19. A mesh can either be user
defined or physics controlled (e.g., 1900b). If a user selects user
controlled mesh, then various additional settings windows may
become available in relation to child nodes of the mesh node. If
the mesh is physics controlled the user may further select an
element size (e.g., 1900c).
[0137] In some aspects, PDEs can be discretized according to the
following process exemplified as a 2-D problem for simplicity. In
some aspects, a starting point for a discretization process is a
weak formulation of the problem.
[0138] Discretization of the constraints identified by Equation 1
can start with the constraints on the boundaries, B.
0=R.sup.(2)on .OMEGA.
0=R.sup.(1)on B
0=R.sup.(0)on P Equation 1
[0139] For each mesh element in B (e.g., each mesh edge in B), the
Lagrange points of some order k are considered and denoted by
x.sub.mj.sup.(1), where m is the index of the mesh element. Then
the discretization of the constraint is
0=R.sup.(1)(x.sub.mj.sup.(1)) Equation 2
where the constraints hold pointwise at the Lagrange points.
[0140] The Lagrange point order k can be chosen differently for
various components of the constraint vector R.sup.(1), and it can
also vary in space. In some aspects of modeling system, such as
multiphysics modeling systems, data structures denote the k as
cporder. The constraints on domains .OMEGA. and points P can be
discretized in the same way. All the pointwise constraints can be
collected in one equation 0=M, where M is the vector including all
the right-hand sides.
[0141] A multiphysics modeling system can approximate the dependent
variables with functions in the chosen finite element space(s).
This means that the dependent variables are expressed in terms of
the degrees of freedom as
u i = i U i .PHI. k ( J ) Equation 3 ##EQU00001##
where .phi..sub.i.sup.(l) are the shape functions for variable
u.sub.l and letting U be the vector with the degrees of freedoms
U.sub.i as its components. This vector can be called the solution
vector because it is include the what is desired to be computed. M
depends only on U.sub.i so the constraints can be written
0=M(U).
[0142] The difference between the discretizing of PDEs on a normal
geometry and a PDE on a product geometry can be in how the shape
functions are expressed. The shape functions can be defined on a
base geometry and an extra geometry. While the above expression may
still be used .phi..sub.i.sup.(l) should be seen as being composed
of the shape functions on the base geometry .psi..sub.a.sup.l and
the shape functions on the extra geometry .theta..sub.b.sup.l. In
some aspects, shape functions can form a product where:
u.sub.1=.SIGMA..sub.a.SIGMA..sub.bU.sub.ab.psi..sub.a.sup.l.theta..sub.b-
.sup.l Equation 4
In the more general case we may view .phi..sub.i.sup.(l) of
Equation 3 as a function of .psi..sub.a.sup.l and
.theta..sub.b.sup.l.
[0143] Now the weak equation is considered:
0 = .intg. .OMEGA. W ( 2 ) A + .intg. B W ( 1 ) s + P W ( 0 ) -
.intg. .OMEGA. .upsilon. h ( 2 ) T .mu. ( 2 ) A - .intg. B
.upsilon. h ( 1 ) T .mu. ( 1 ) s - P .upsilon. h ( 0 ) T .mu. ( 0 )
Equation 5 ##EQU00002##
where .mu..sup.(i) are the Lagrange multipliers.
[0144] To discretize the weak equation, the dependent variables are
expressed in terms of the DOFs as described earlier. Similarly, the
test functions can be approximated with the same finite elements
(this is the Galerkin method):
.upsilon. l = i V i .PHI. i ( J ) Equation 6 ##EQU00003##
[0145] Because the test functions occur linearly in the integrands
of the weak equation, it can be enough to specify that the weak
equation holds when the test functions are chosen as shape
functions:
u.sub.l=.phi..sub.i.sup.(l) Equation 7
When substituted into the weak equation, this gives one equation
for each i.
[0146] Now the Lagrange multipliers can be discretized. Let
.LAMBDA..sub.mj.sup.(d)=.mu..sup.(d)(x.sub.mj.sup.(d)).omega..sub.mj.sup-
.(d) Equation 8
where x.sub.mj.sup.(d) are the Lagrange points defined earlier, and
.omega..sub.mj.sup.(d) are certain weights, as discussed elsewhere
in more detail. The term
.intg. R .PHI. i h ( 1 ) T .mu. ( 1 ) s Equation 9 ##EQU00004##
is approximated as a sum over all mesh elements in B.
[0147] The contribution from mesh element number m to this sum is
approximated with the Riemann sum
j .PHI. i ( x mj ( 1 ) ) h ( 1 ) T ( x mj ( 1 ) ) .mu. ( 1 ) ( x mj
( 1 ) ) .omega. mj ( 1 ) = j .PHI. i ( x mj ( 1 ) ) h ( 1 ) T ( x
mj ( 1 ) ) .LAMBDA. mj ( 1 ) Equation 10 ##EQU00005##
where .omega..sub.mj.sup.(1) is the length (or integral of ds) over
the appropriate part of the mesh element. The integral over .OMEGA.
and the sum over P can be similarly approximated.
[0148] The above operation can yield the following discretization
of the weak equation:
0=L-N.sub.F.LAMBDA. Equation 11
where L is a vector whose ith component is
.intg. .OMEGA. W ( 2 ) A + .intg. R W ( 1 ) s + P W ( 0 ) Equation
12 ##EQU00006##
evaluated for
u.sub.l=.phi..sub.i.sup.(l) Equation 13
.LAMBDA. is the vector including all the discretized Lagrange
multipliers .LAMBDA..sub.mj.sup.(d).LAMBDA..sup.mj.sup.(d). N.sub.F
is a matrix whose ith row is a concatenation of the vectors
.phi..sub.i(x.sub.mj.sup.(d))h.sup.(d)(x.sub.mj.sup.(d)).sup.T
Equation 14
[0149] For problems using ideal constraints, N.sub.F is equal to
the constraint Jacobian matrix N, which is defined as
N = .differential. M .differential. U Equation 15 ##EQU00007##
[0150] To sum up, in some aspects, the discretization of the
stationary problem is
0=L(U)-N.sub.F(U).LAMBDA.
0=M(U) Equation 16
[0151] It is contemplated that an objective of the above operation
is to solve this system for the solution vector U and the Lagrange
multiplier vector .LAMBDA.. L is called the residual vector, M is
the constraint residual, and N.sub.F is the constraint force
Jacobian matrix. M is redundant in the sense that some pointwise
constraints occur several times. Similarly, .LAMBDA. is redundant.
Equations solvers remove this redundancy.
[0152] The integrals occurring in the components of the residual
vector L (as well as K, as discussed elsewhere herein) are computed
approximately using a quadrature formula. Such a formula can
compute the integral over a mesh element by taking a weighted sum
of the integrand evaluated in a finite number of points in the mesh
element. The order of a quadrature formula on a 1-D, triangular, or
tetrahedral element is the maximum number k such that it exactly
integrates all polynomials of degree k. For a quadrilateral
element, a formula of order k integrates exactly all products
p(.xi..sub.1)q(.xi..sub.2), where p and q are polynomials of degree
k in the first and second local coordinates, respectively. A
similar definition can be applied for hexahedral and prism
elements. The accuracy of the quadrature can increase with the
order, while the number of evaluation points also increases with
the order, as well. As a rule of thumb, in some aspects the order
may be twice the order of the shape function for the finite element
being used. In some aspects, multiphysics data structures can refer
to the order of the quadrature formula as gporder, where gp denotes
Gauss points. In certain aspects, the maximum available order of
the quadrature formula (the gporder value) may be (i) 41 for 1-D,
quadrilateral, and hexahedral meshes; (ii) 30 for triangular and
prism meshes; and (iii) 8 for tetrahedral meshes.
[0153] Discretization of a time-dependent problem may be similar to
a stationary problem
0=L(U,{dot over (U)},U,t)-N.sub.F(U,k).LAMBDA.
0=M(U,k) Equation 17
where U and .LAMBDA. now depend on time t.
[0154] Now, considering a linearized stationary problem, the
linearization "point" u.sub.o corresponds to a solution vector
U.sub.0. The discretization of the linearized problem is
K(U.sub.0)(U-U.sub.0)+N.sub.F(U.sub.0).LAMBDA.=L(U.sub.0)
N(U.sub.0)(U-U.sub.0)=M(U.sub.0) Equation 18
where K is called the stiffness matrix, and L(U.sub.0) is the load
vector. For problems given in general or weak form, K is the
Jacobian of -L:
K = - .differential. L .differential. U Equation 19
##EQU00008##
[0155] The entries in the stiffness matrix can be computed in a
similar way to the load vector, namely by integrating certain
expressions numerically. This computation is called the assembling
the stiffness matrix.
[0156] If a problem is linear, then its discretization can be
written
KU+N.sub.F.LAMBDA.=L(0)
NU=M(0) Equation 20
[0157] Similarly, for a time-dependent model the linearization
involves the damping matrix
D = .differential. L .differential. U Equation 21 ##EQU00009##
and the mass matrix
E = - .differential. L .differential. U _ Equation 22
##EQU00010##
When E=0, the matrix D is often called the mass matrix instead of
the damping matrix.
[0158] Discretization of an eigenvalue problem is
.lamda..sup.2E(U.sub.0)U+K(U.sub.0)U+N.sub.F(U.sub.0).LAMBDA.=0
N(U.sub.0)U=0 Equation 23
where U.sub.0 is the solution vector corresponding to the
linearization "point." If the underlying problem is linear, then D,
K, and N do not depend on U.sub.0, which yields:
KU+N.sub.F.LAMBDA.=.lamda.DU-.lamda..sup.2EU
NU=0 Equation 24
[0159] In some aspects, weak constraints provide an alternative way
to discretize the Dirichlet conditions, as opposed to the pointwise
constraints described earlier. The idea is to regard the Lagrange
multipliers .mu..sup.(d) as field variables and thus approximate
them with finite elements. This concept also introduces
corresponding test functions v.sup.(d). Multiplying the Dirichlet
conditions with these test functions and integrating gives the
following system, in the case of a stationary problem in 2-D:
0 = .intg. .OMEGA. W ( 2 ) A + .intg. R W ( 1 ) s + P W ( 0 ) -
.intg. .OMEGA. .upsilon. h ( 2 ) T .mu. ( 2 ) A - .intg. R
.upsilon. h ( 1 ) T .mu. ( 1 ) s - P .upsilon. h ( 0 ) T .mu. ( o )
0 = .intg. .OMEGA. v ( 2 ) R ( 2 ) A 0 = .intg. R v ( 1 ) R ( 1 ) s
0 = P v ( o ) R ( o ) Equation 25 ##EQU00011##
[0160] These weak equations can be combined to form a single
equation. This treatment of the Lagrange multipliers as ordinary
variables can produce a weak equation without constraints. This can
be useful if the Lagrange multipliers are of interest in their own
right.
[0161] It is contemplated that combining pointwise and weak
constraints unique situations can arise. For example, if both types
of constraints are present for some variable, and the constraints
are in adjacent domains, the resulting discretization may not work.
Instead, it is contemplated that pointwise constraints can be
obtained from the weak constraints formulation by using the shape
functions
.delta.(x-x.sub.mj.sup.(d)) Equation 26
for the Lagrange multipliers and their test functions, that is,
let
.mu. ( d ) = m , j .LAMBDA. mj ( d ) .delta. ( x - x mj ( d ) )
Equation 27 ##EQU00012##
where .delta. is Dirac's delta function.
[0162] In some aspects, physics interfaces in modeling systems can
be operable to predefine dependent variables on product geometries.
This is can be a desirable aspect as exemplified below.
[0163] An exemplary aspect of the present disclosure can include a
structural shell interface where a user describes the thickness
direction of a shell as an extra dimension and a surface
constituting a base geometry. In general, a shell element
discretization is suited for structures which are thin in one
direction. The displacement, stresses, and strains may be described
by displacement and rotation physical quantities located on the
mid-surface of the shell. Such a mid-surface may be described using
a base model including a three-dimensional surface constituting a
base geometry. The three-dimensional surface may be curved in a
three dimensional space. For linear elastic problems, this may be
the only information needed for solving a structural problem, since
the shell theory assumptions allows for an analytical
representations of the variations of all structural quantities in
the thickness direction.
[0164] An extra dimension can be introduced when some physical
quantity varies along the thickness and when this variation may not
be handled analytically. It may also be introduced as a convenience
for describing a variation in material in the shell for instance
for multi layered shells. The thickness direction is then described
as a line segment which is an extra geometry. The extra geometry
may form a product geometry with the base geometry and the relevant
physical quantities may then be defined on the product geometry.
There are two situations where such an approach may be used for
structural shells. The first is where stiffness contributions from
different levels in the shell cannot be analytically integrated
through the thickness. This would for example be the case for a
nonlinear elastic or hyperelastic materials. In this case an extra
dimension can be used to integrate nonlinear functions through the
thickness, that is, the extra geometry. The second is where state
variables are computed and stored at different levels in the shell
thickness direction. This would be the situation for e.g.
elastoplastic and creep materials. The concept is examined more in
detail below in the context of creep materials.
[0165] For a material which experiences creep, the rate of the
creep strain tensor ({dot over (.epsilon.)}.sub.c) can be described
as
{dot over (.epsilon.)}.sub.c=f(.theta.,T,t) Equation 28
Here, .sigma. denotes the stress tensor, T the temperature, and t
the time. The function .LAMBDA. is usually strongly nonlinear. The
creep strain tensor is symmetric, and will thus have six
independent components. Since the stress state, and possibly also
the temperature, will vary through the thickness of the shell, the
creep strain rate will have a strong variation with the local
coordinate through the thickness (.zeta.).
[0166] The constitutive law used for computing the stresses is
.sigma.=D:(.epsilon.-.epsilon..sub.c) Equation 29
where : denotes inner product. D is the fourth order elastic
constitutive tensor and .epsilon. is the total strain tensor which
is computed from the displacements and rotations at the mid-surface
of the shell. To compute the stress and the Jacobians for the
stiffness matrix, creep strain should be available through the
thickness. The expressions, variables and parameters may be
expressed in a symbolic form in a GUI in a physics or multiphysics
simulation system. Furthermore, predefined expressions can be user
editable.
[0167] Other physical quantities such as temperature and heat flux
may also be described in physics interfaces using PDEs. In these
PDEs, physical properties may be expressed as functions of physical
quantities in PDEs defined on the product geometry. These PDEs may
form a coupled system of PDEs, together with the PDEs describing
the structural problem (including, for example creep strain). The
PDEs of such a coupled system may be user editable.
[0168] The extra geometry, which is in the thickness direction, may
be discretized and form a product geometry with the discretized
base geometry. The PDEs describing the structural problem may be
discretized together with PDEs describing other physical quantities
and may then be expressed as degrees of freedom on the discretized
product geometry. The shape functions selected for the structural
problem can have any type of continuity in the direction along the
thickness.
[0169] The structural problems may be solved independently or
together with equations for other physical quantities using a
numerical solver. A user may thus be able to model creep strain
independently or coupled to other physical quantities (described in
other physics interfaces) in a shell interface by describing the
thickness direction using an extra geometry, said extra geometry
forming a product geometry with the base geometry.
[0170] It may be desirable to model multi-layer shells using an
extra geometry to construct product geometries. In particular, it
may be beneficial to describe the thickness direction using either
a materials section feature, including functionality for describing
layered structures, or by including such edit fields in for example
a settings window for a shell physics interfaces.
[0171] Another exemplary aspect includes a structural beam
interface. The same considerations as for shells apply. The
difference is that the standard beam formulation introduces
displacements and rotations along a line or a curve. A 2-D extra
geometry can be specified for representing the beam cross section
and nonlinear functions or state variables may be described in the
cross section.
[0172] For the structural beam aspect, a base geometry can be
constructed as a line segment or curve segment, which may be curved
or twisted in a 3-D space. The extra geometry representing the
cross section may be loaded from a file, obtained from a library of
beam cross sections, or constructed using the tools for creating
geometries described elsewhere. It is also possible that the cross
section is described by referring to a beam cross-section defined
in a materials section described elsewhere. A product geometry is
formed between the base geometry and the extra geometry. Various
user editable expressions describing physical quantities, for
instance the creep strain tensor are defined on the product
geometry, in the form of PDEs, possibly forming a coupled system
with other PDEs. The model is discretized analogously to the shell
example and solved either independently or as the coupled system
using a numerical solver. A user may thus be able to model creep
strain independently or coupled to other physical quantities
(described in other physics interfaces) in a structural beam
interface by describing the cross section using an extra geometry,
said extra geometry forming a product geometry with the base
geometry.
[0173] Yet another exemplary aspect is a packed bed reactor which
can be modeled using a base geometry and forming a product geometry
with an extra geometry. The packed bed reactor is one of the most
common reactors in the chemical industry, for use in heterogeneous
catalytic processes. Such a reactor may include a container filled
with catalyst particles. These particles may be supported by a
structure, like tubes or channels, or they can be packed in one
single compartment in the reactor. Some of the complexities of
modeling mass and energy transport in a reactor lies in the
description of the porous structure, which gives transport of
different orders of magnitudes within the particles and between the
particles. In most situations, the structure between particles is
described as macroporous structure and the particle radius can be
of the order of magnitude of 1 mm. When a pressure difference is
applied across the bed, convection arises in the macroporous bulk
of the reactor. The pores inside the catalyst particles form the
microstructure of the bed and transport in this microstructure
takes place mainly in the form of diffusion. By applying an extra
dimension approach, a time dependent model can provide the mass and
reaction distributions in the reactor and within each catalyst
pellet in the reactor. This makes it possible to evaluate the
utilization of catalyst load, optimal pellet size, or inlet
temperature.
[0174] A model can be defined for a reactor where the pressure
drop, convection, and diffusion takes place in three-dimensions.
Assuming that the particles are spherical, only the transport and
reactions along the radius may be specified in a model. Different
dimensionalities with respect to the reactor and pellets would use
a similar approach.
[0175] Referring now to FIGS. 20-29, an exemplary aspect of the
simulation methods for modifying a geometry of a model according to
the present disclosure are illustrated in the context of propylene
and carbon monoxide being oxidized in catalytic particles.
[0176] FIG. 20 includes exemplary equations and parameters
describing modeled reactions, according to some aspects of the
present disclosure. Equations of reactions are provided for the
catalyzed oxidation of carbon monoxide to carbon dioxide 2000a and
the catalyzed oxidation of propylene to water and carbon dioxide
2000b. The reaction rate for equation 2000a is provided at element
2000c and the reaction rate for equations 2000b is provided at
element 2000d. Rate constants may be calculated using the Arrhenius
equation 2000e. Values for the activation energy E and the
frequency factor A are provided in table 2000f.
[0177] FIG. 21 includes exemplary equations describing physical
properties of species in the reactor bulk, according to some
aspects of the present disclosure. For example, the total
concentration and flow velocity may be described by the continuity
equation 2100a, where c is the total concentration which is the
concentration of all species including the solvent 2100h, t is the
time, u is the reactor flow velocity, and s a sink/source term
reflecting that while atoms are not created or destroyed, the
number of molecules may vary due to reactions. The pressure
gradient in the reactor is related to the flow velocity through
Darcy's law 2100b, where P denotes pressure, k is the permeability
of the packed bed reactor, and .eta. is the viscosity of the gas
flowing through the reactor. The total molecular flux is the sum of
the flux of each species N.sub.i 2100c. The species flux in the
reactor may include a diffusion and a convection contribution as
provided in 2100d, where D.sub.i is the diffusion tensor and
c.sub.i is the concentration of species i. The convection and
diffusion equation is provided in 2100e, where R.sub.i is a source
term, reflecting the contribution by reactions and transport within
the catalyst particles. Boundary conditions at the reactor inlet
are provided in 2100f. At the outlet of the reactor convective mass
transport is dominant and can give a second boundary condition
2100g, where n is the outward vector unit normal.
[0178] Referring back to the convection and diffusion equation
2100e, the source term, R.sub.i, depends on the transport inside
the catalyst particles. The molar flux at the outer surface of the
particles multiplied by the available outer surface area of the
particles per unit volume can provide a proper source term. It can
be desirable to apply an extra dimension to model the catalyst
particles to obtain the source term R.sub.i.
[0179] FIG. 22 includes exemplary equations describing physical
properties of species in the porous particles of a modeled reactor,
according to some aspects of the present disclosure. It is
contemplated for the exemplary model of the species in the bulk
reactor that inside the particles there is no convection
contribution, only diffusion. The contribution to the species
concentration is provided in 2200a. c.sub.pi is the concentration
of i in the catalyst particle. D.sub.pi is the diffusion tensor (in
this example a scalar) for species i within the particle while
R.sub.p is the reaction rate for the heterogeneous reaction in the
particle. A boundary condition stating that net outward diffusion
at the center of the particle is 0 is provided in 2200b, and a
boundary condition stating that the species concentration within
the particle is equal to the reactor bulk species concentration,
adjusted by the porosity .epsilon. of the particle is provided in
2200c. An expression for the source term R.sub.i is provided in
2200d. The expression in 2200d for the exemplary model is valid at
the particle surface, where the independent radius variable r
equals the particle radius, r.sub.p. A.sub.p denotes the pellet
surface to volume ratio.
[0180] It is contemplated that for this exemplary model a product
geometry between a base geometry for the reactor and an extra
geometry for catalyst particles can provide a way to accurately
model the interface between the concentrations on the outside of
the pellets and those on the inside. In this exemplary model, the
physics interface for transport of diluted species can be used to
model the packed bed reactor. Such a physics interface may include
processes for automatically constructing extra dimensions, for
particle radius, and forming a product geometry automatically.
[0181] FIGS. 23A-23C illustrate exemplary menus and settings
windows for creating geometries describing a bulk reactor as a base
geometry and particles as an extra geometry, according to some
aspects of the present disclosure. For example, a user of the
modeling system draws a shape 2300a to represent the reactor, and
which may also represent the base geometry. The user can then set
the radius 2300b for the catalytic particle in a settings window of
a physics interface. The system can then automatically construct a
line segment dependent on the radius as an extra geometry, In some
aspects, a graphical representation of the particle can
alternatively be constructed in a geometry settings window 2300c. A
product geometry can then be formed between the base geometry and
the extra geometry.
[0182] FIGS. 24-30 illustrate exemplary settings windows and
results for modeling a reactor including porous particles described
as an extra geometry, according to some aspects of the present
disclosure. In FIGS. 24A-24B, parameters can be set by a user by
entering the data into edit fields 2400a, or by loading them into a
memory from a file. The reaction rates are then defined along with
certain other variables 2400b, which can also be defined on the
product geometry.
[0183] It is contemplated that physics interfaces, such as the
interface illustrated in FIG. 25, can include several child nodes
2500a, where each child node can include one or more settings
windows. These settings windows can include sections for specifying
input for the bulk of the reactor, and sections for specifying
input for the catalytic particles. Two sets of diffusion tensors
2500b, 2500c, or scalar diffusion coefficients for isotropic
materials, can be defined, one set for the reactor 2500b and one
set for the catalytic particles 2500c. In the same settings window,
convection can also be defined. A modeling software can then
automatically assigns the diffusion coefficient and convection
expressions for the reactor to the base geometry and the diffusion
coefficient for the particles to the extra geometry.
[0184] In some aspects, another settings window, such as settings
window 2600a in FIG. 26, can be accessed where initial
concentrations can be defined on each geometry. It is also
contemplated that boundary conditions 2700a and reactions 2800a in
the particles as well as the flux 2800b from the particles into the
reactor bulk can also be defined as exemplified by the setting
windows of FIGS. 27 and 28.
[0185] The expressions and variables can be assigned on the product
geometry as predefined by the physics interfaces. It is
contemplated that the generated PDEs, which may be expressed in
weak form (e.g., 2900a in FIG. 29), can further be user editable.
The user can then mesh the base geometry representing the reactor.
The extra dimension can be automatically meshed in accordance with
predefined settings in the physics interfaces. In some aspects, the
extra dimension mesh can be user defined. Two meshes can then be
generated. One mesh is generated for the base geometry and one for
the extra geometry. A compute icon 3000a can then be selected, as
exemplified in FIG. 30, to solve the model. The modeling system can
solve the equations for the dependent variables, representing
physical quantities such as concentration and temperature in the
reactor bulk and in the catalytic particles. The user may construct
various plots 3000b as exemplified in FIG. 30, or tables to view
representations of the solution.
[0186] Another exemplary aspect of the simulation methods for
modifying the geometry of a model according to the present
disclosure are illustrated in the context of absorption and
scattering of radiation in a participating media are illustrated,
according to some aspect of the present disclosure. Referring now
to FIG. 31, for a given wavelength, the intensity of radiation in
position s and in direction .OMEGA. can be determined by applying
the equation provided at 3100a, where .kappa., .beta., and
.sigma..sub.s denote absorption, extinction, and scattering
coefficients, respectively. I(.OMEGA., s) denotes the radiation
intensity at the position s position in the .OMEGA. direction. For
radiation in heat transfer, the first term of the equation at 3100a
relates to the blackbody radiation intensity which is represented
by the expression provided at 3100b, where n refers to the
refractive index. The second term of the equation at 3100a refers
to extinction and the third term to scattering. It can be desirable
to introduce extra dimensions to model the system represented by
the equations because of the high dimensionality of a phase space.
Given a three dimensional geometry, there are three dimensions for
defining s. The direction .OMEGA. may be described by two angles
adding two dimensions and an additional dimension can be added for
wavelength, and the additional dimension may be used for radiation
with multiple wavelengths.
[0187] A user modeling the above example can construct a base
geometry that describes the three-dimensional space. An extra
geometry may be predefined in the physics interface as a sphere,
spanned by the two angles rotation, with an independent variable
along the radius representing the wavelength of radiation. The
extra geometry may or may not be displayed in the GUI depending on
the settings of the modeling system. The physics interface can
include settings windows for model inputs that may be typed in edit
fields or selected from lists. Such input may be for instance,
temperature field variable, absorption coefficients, scattering
coefficients, and scattering type describing the phase function of
the scattering. Some inputs may be given by defining a material on
the base geometry or on parts of the base geometry. Examples of
such inputs are absorption and scattering coefficients. Materials
used in the model may be defined in certain aspects only on the
base geometry, and the modeling system may automatically handle the
formation of product geometries. Radiation can be described as
editable PDEs. Other physical quantities may be described either in
the physics interface for radiation or in other physics interfaces.
Such physical quantities can also be expressed as editable PDEs and
may form a system of coupled PDEs with the PDEs describing
radiation. The PDEs of the radiation interface may be discretized
and solved either independently or as the coupled system of partial
differential equations using finite element solvers. A user may
thus model radiation in participating media, either independently
or coupled to other physical quantities, by describing the
direction of radiation and possibly wavelength of the radiation
using an extra geometry. The extra geometry can form a product
geometry with the base geometry describing the space in which
radiation is modeled.
[0188] Yet another exemplary aspect is a physics interface for
simulating a gas. The physics interface can be referred to as a
Boltzmann interface. Such models may define the time dependent
Boltzmann equation for describing the spatial distribution and
velocity distribution of the particles of a gas. The Boltzmann
equation gives the probability of finding particles within a volume
element dx centered at position x and within a certain velocity
range dv centered on a velocity v within a given time range.
Similarly to the case of radiation, the phase space has a
dimensionality of six for a gas modeled in a 3D geometry. A
position in space may be described by a base geometry while the
velocity may be described by extra dimensions. The base geometry
may be three-dimensional, describe by three space coordinates,
while the extra dimensions for the velocity may be described by the
volume of a sphere, with one independent variable (the radius)
describing the speed of the particles, and two other independent
describing the angular dependency of the speed (the sphere spanned
by rotating the two angles), together giving the velocity of a
particle in a given direction.
[0189] When modeling a system where there is a sufficient range in
the difference between the masses of the particles, it can be
desirable to create several extra geometries. Each extra geometry
can describe particles within a certain mass range, and thereby
introduce an independent variable also for mass. It is also
contemplated that a variation in mass can be introduced as yet
another extra dimension.
[0190] A user can construct a base geometry describing a space
including the particles. The Boltzmann interface may construct one
or more extra geometries automatically, the dimensionality of the
extra geometries dependent on the base geometry. The extra
geometries can form a product geometry with the base geometry
automatically as predefined by the Boltzmann interface. The user
may give inputs to the Boltzmann interface, the inputs being
specified for example by typing in edit fields or making selections
in lists. The user may give inputs for instance relating to
particle types, temperature, pressure and number of particles.
Physical quantities in the Boltzmann interface may be predefined by
user editable expressions in the form of PDEs.
[0191] It is contemplated that other physical quantities can be
described either in the Boltzmann interface or in other physics
interfaces. Such physical quantities can be expressed as editable
PDEs or ODEs and may form a system of coupled PDEs together with
the PDEs describing the spatial and velocity distribution of the
gas. The PDEs of the Boltzmann interface may be discretized and
solved either independently or as the coupled system of partial
differential equations using a numerical solver. A user may thus
model a time dependent spatial and velocity distribution of a gas
either independently or coupled to other physical quantities by
describing the velocity distribution using extra geometries with
the extra geometry forming a product geometry with the base
geometry describing the spatial distribution.
[0192] A further exemplary aspect of the present disclosure is an
automatic operation for attaching PMLs to a geometry using extra
geometries. A PML may exist on the boundaries of a wave equation to
model that the wave is absorbed with no reflection on the boundary.
For simplicity, a user of the modeling system can constructs a
rectangle in a physics interface modeling some type of wave
propagation phenomenon. Two parallel boundaries of the rectangle
can be referred to as being directed in the x-direction and the
other two boundaries of the rectangle as being directed in the
y-direction. The user may select the boundaries of the rectangle
and define the boundaries of the rectangle as perfectly matched
layers. The modeling system can then automatically construct two
extra geometries in the form of line segments, for example denoted
XDx and XDy. The modeling system can further create several product
geometries. XDx may form two 2-D product geometries with the
boundaries directed in the x-direction. XDy may form two 2-D
product geometries with the boundaries directed in the y direction.
XDx and XDy may form a product of extra dimensions. The product of
extra dimensions can form four 2-D product geometries with the
vertexes of the rectangle. An example of a coordinate stretching
transformation is
.xi. = sign ( .xi. - .xi. 0 ) .xi. - .xi. 0 n L .delta. .xi. n ( 1
- l ) Equation 30 ##EQU00013##
where the PML scaling factor and n can be determined by the
modeling system and may further be user editable along with .xi.
and .xi..sub.0. A coordinate stretching transformation can further
be applied to the product geometries.
[0193] According to some aspects, a simulation method is executed
in a computer system with one or more processors configured to
modify a geometry of a model of a physical system including
physical quantities represented in terms of a combined set of
equations. The simulation method comprising the acts of defining
geometry data representing a geometry of a physical system
represented by a first combined set of equations. The geometry data
is associated with a first model of the physical system. Extra
geometry data representing one or more extra geometries for a
modified model based on the first model is defined, via one or more
processors. A first set of geometric entity data representing one
or more geometric entities of the geometry of the physical system
from which to extend the one or more extra geometries is determined
via at least one of the one or more processors. At least a portion
of the extra geometry data representing at least one of the one or
more extra geometries is added, via at least one of said one or
more processors, to the determined first set of geometric entity
data representing one or more geometric entities by forming product
geometry data representing a product geometry for the modified
model. The extra geometry data representing the one or more extra
geometries is at least a part of the product geometry data.
Non-discretized equation data representing a non-discretized second
combined set of equations for at least a portion of the product
geometry data is generated via at least one of the one or more
processors. Optionally a graphical representation of at least a
portion of the product geometry data is generated. The graphical
representation is configured for display on a graphical user
interface.
[0194] It is contemplated that the simulation method described
above can further include in some aspects one or more of the
following features. At least a portion of the product geometry data
can be stored as graphical representations configured for later
display on one or more display devices. The method can also include
generating a graphical representation of at least a portion of the
product geometry data, with the graphical representation configured
for display on one or more display devices. The graphical
representation can include at least a portion of the product
geometry data. The one or more extra geometries can be a part of an
extra dimension. The simulation method can further include the act
of determining, via at least one of said one or more processors, a
second set of geometric entity data representing one or more
geometric entities of the one or more extra geometries, and
determining product selection data representing a product of
selections computed as a Cartesian product between at least a
portion of the first set of geometric entity data representing one
or more geometric entities of the geometry and at least a portion
of the second set of geometric entity data representing one or more
geometric entities of the one or more extra geometries. The
non-discretized equation data representing the non-discretized
second combined set of equations can be user editable to allow
editing of the second combined set of equations. The updated
combined set of equations can be a combined set of non-discretized
differential equations. The non-discretized second combined set of
equations can be a combined set of non-discretized partial
differential equations configured as input data for a partial
differential equation solver.
[0195] It is further contemplated that the simulation method
described above can also include in some aspects one or more of the
following features. At least one of the one or more geometric
entities can be a vertex, an edge, a boundary, or a domain. The
simulation method can further include the act of defining material
property data representing a material property for at least one of
the one or more extra geometries. The simulation method can also
include the act of defining material property data representing a
material property for at least a portion of the product geometry
data after forming the product geometry data representing the
product geometry for said modified model. The geometry of the
physical system can be one-dimensional and the one or more extra
geometries are two-dimensional. The geometry of the physical system
can also be three-dimensional and the one or more extra geometries
can be one-dimensional. The geometry of the physical system and the
one or more extra geometries can both be three-dimensional. The
determining of the first set of geometric entity data representing
one or more geometric entities on the geometry of a physical system
can be based on user selections received via a graphical user
interface. Similarly, the determining of the second set of
geometric entity data representing one or more geometric entities
of the one or more extra geometries can be based on user selections
received via a graphical user interface. Defining of the geometry
data representing the geometry of the physical system can include
extracting the geometry data from data representing the first model
of the physical system. Defining of the extra geometry data
representing one or more extra geometries can occur at least in
part via selections of extra geometry properties received via a
graphical user interface.
[0196] According to some aspects, a simulation system or apparatus
is contemplated for adding extra geometries to a base geometry of a
model of a physical system represented in terms of a combined set
of differential equations. The system includes one or more physical
memory devices, one or more display devices, one or more user input
devices, and one or more processors are configured to or adapted to
execute instructions stored on at least one of the one or more
physical memory devices. The instructions cause at least one of the
one or more processors to perform steps including defining base
geometry data representing a base geometry of a physical system.
The base geometry data is associated with a first model of the
physical system, which is represented by a combined set of
differential equations. Extra geometry data is defined representing
one or more extra geometries for a modified model based on said
first model. A first set of geometric entity data is determined
representing one or more entities of the base geometry from which
to extend the one or more extra geometries. At least a portion of
the extra geometry data representing at least one of the one or
more extra geometries is added to the determined first set of
geometric entity data representing one or more entities of the base
geometry by generating product data representing a product geometry
for the modified model. The extra geometry data is at least a part
of the product data. Equation data is generated representing an
updated combined set of differential equations for the modified
model that includes at least a portion the product data. The
equation data and the product data can be stored in at least one of
the one or more physical memory devices.
[0197] It is contemplated that the simulation system or apparatus
described above can further include in some aspects one or more of
the following features. At least a portion of the product data can
be stored as graphical representations configured for later display
on the one or more display devices. The instructions can also cause
at least one of the one or more processors to further perform a
step comprising generating a graphical representation of at least a
portion of the product data, where the graphical representation is
configured for display on at least one of the one or more display
devices. At least a portion of the product data can be stored as
graphical representations configured for later display on the one
or more display devices. The instructions can further cause at
least one of the one or more processors to perform a step
comprising generating a graphical representation of at least a
portion of the product data where the graphical representation
configured for display on at least one of the one or more display
devices. The graphical representation can include the at least a
portion of the product geometry data. The determining of the first
set of geometric entity data representing one or more geometric
entities on the geometry of a physical system can be based on user
selections received via a graphical user interface. The defining of
the geometry data representing the geometry of the physical system
can include extracting the geometry data from data representing the
first model of the physical system. The defining of the extra
geometry data representing of one or more extra geometries can
occurs at least in part via selections of extra geometry properties
received via a graphical user interface.
[0198] It is further contemplated that the simulation system or
apparatus described above can also include in some aspects one or
more of the following features. The one or more extra geometries
can be a part of an extra dimension. The system or apparatus can
further include the act of determining, via at least one of the one
or more processors, a second set of geometric entity data
representing one or more geometric entities of the one or more
extra geometries, and determining product selection data
representing a product of selections that can be computed as a
Cartesian product between at least a portion of the first set of
geometric entity data representing one or more geometric entities
of the geometry and at least a portion of the second set of
geometric entity data representing one or more geometric entities
of the one or more extra geometries. The non-discretized equation
data representing the non-discretized second combined set of
equations can be user editable to allow editing of the second
combined set of equations. The updated combined set of equations
can be a combined set of non-discretized differential equations.
The non-discretized second combined set of equations is a combined
set of non-discretized partial differential equations configured as
input data for a partial differential equation solver. At least one
of the one or more geometric entities can be a vertex, edge,
boundary, or a domain. The system or apparatus can further include
the act of defining material property data representing a material
property for at least one of the one or more extra geometries. The
system or apparatus can further include defining the material
property data representing a material property for at least a
portion of the product geometry data after forming the product data
representing the product geometry for the modified model. The
geometry of the physical system can be one-dimensional and the one
or more extra geometries can be two-dimensional. The geometry of
the physical system can also be three-dimensional with the one or
more extra geometries being one-dimensional. The geometry of the
physical system and the one or more extra geometries can further
both be three-dimensional.
[0199] According to some aspects, a simulation apparatus or system
for adding extra geometries to a model of a physical system is
contemplated. The apparatus or system includes a physical computing
system comprising one or more processors, one or more user input
devices, a display device, and one or more memory devices. At least
one of the one or more memory devices includes executable
instructions for modifying a geometry of a model of a physical
system represented in terms of a combined set of equations. The
executable instructions cause at least one of the one or more
processors to perform, upon execution, acts comprising receiving a
base geometry of said physical system in response to one or more
first inputs received via the one or more user input devices. The
base geometry is associated with a model of the physical system
which is represented in terms of a combined set of equations. One
or more second inputs are received via at least one of the one or
more user input devices. The second inputs define one or more extra
geometries associated with the base geometry. One or more first
geometric entities of the base geometry and one or more second
geometric entities of the extra geometry are determined. At least
one of the one or more extra geometries are added to the base
geometry by computing a product geometry of the determined one or
more first geometric entities and the one or more second geometric
entities. The one or more extra geometries are at least a part of
the product geometry. An updated combined set of equations is
generated including representations of at least a portion of the
product geometry. A graphical representation is generated of at
least a portion of the product geometry. The graphical
representation is configured for display on the display device.
[0200] It is contemplated that the simulation apparatus or system
described above can further include in some aspects one or more of
the following features. The updated combined set of equations can
be a combined set of non-discretized differential equations. At
least a portion of the product geometry can be stored as graphical
representations configured for later display on the one or more
display devices. The graphical representation can include at least
a portion of the product geometry. The one or more extra geometries
can be a part of an extra dimension. The computing of the product
geometry can be implemented as a Cartesian product between at least
a portion of the one or more first geometric entities of the base
geometry and one or more second geometric entities of the one or
more extra geometries. The updated combined set of equations can be
user editable to allow editing of the second combined set of
equations. The updated combined set of equations can be a combined
set of non-discretized partial differential equations configured as
input data for a partial differential equation solver. At least one
of the one or more first geometric entities can be a vertex, an
edge, a domain, or a boundary. The system or apparatus can also
define a material property for at least one of the one or more
extra geometries. In addition, the system or method can define a
material property for at least a portion of the product geometry
after computing the product geometry. The geometry of the physical
system can be one-dimensional and one or more extra geometries can
be two-dimensional. The geometry of the physical system can also be
three-dimensional with the one or more extra geometries being
one-dimensional. The geometry of the physical system and the one or
more extra geometries can both be three-dimensional. The
determining of the one or more first geometric entities on the base
geometry of a physical system can be based on user selections
received via a graphical user interface. The defining of the base
geometry of the physical system can include at least partially
extracting the base geometry from data representing the model of
the physical system. The defining of one or more extra geometries
can occur at least in part via selections of extra geometry
properties received via a graphical user interface.
[0201] Certain aspects of the present disclosure contemplate
methods, systems, or apparatus based on any and all combinations of
any two or more of the steps, acts, or features, individually or
collectively, disclosed or referred to or otherwise indicated in
the present disclosure.
[0202] The exemplary aspects for simulation methods, apparatus, and
systems for modifying a geometry, for adding extra geometries to a
base geometry, and for adding geometries to model(s) of physical
system(s) presented in FIGS. 1-31 are merely examples and are
understood to apply to broader applications and physic phenomena,
not just the simulation aspects described in more detail or
illustrated in the figures. For example, it would be understood
that many different custom geometries depending on a particular
application can be modified or extra geometries added thereto using
the present disclosures. The illustrated aspects are merely
examples of the broader operations that may be performed by a
modeling system. Furthermore, other types of graphical, user, or
alternative input-type interfaces are contemplated.
[0203] Referring now to FIG. 32, an exemplary aspect of a computer
system is illustrated that may be used with the methods described
elsewhere herein including modeling systems and systems for
generating a modified geometry of a model of a physical system. The
computer system 3210 includes a data storage system 3212 connected
to host systems 3214a-3214n through communication medium 3218. In
this embodiment of the computer system 3210, the "n" hosts
3214a-3214n may access the data storage system 3212, for example,
in performing input/output (I/O) operations. The communication
medium 3218 may be any one of a variety of networks or other type
of communication connections as known in the modeling and computer
simulation field. For example, the communication medium 3218 may be
the Internet, an intranet, or other network connection by which the
host systems 3214a-114n may access and communicate with the data
storage system 3212, and may also communicate with others included
in the computer system 3210, including without limitation systems
based on various forms of network communications (e.g., fiber
optic, wireless, Ethernet).
[0204] Each of the host systems 3214a-3214n and the data storage
system 3212 included in the computer system 3210 may be connected
to the communication medium 3218 by any one of a variety of
connections as may be provided and supported in accordance with the
type of communication medium 3218. The processors included in the
host computer systems 3214a-3214n may be any one of a variety of
commercially available single or multi-processor system, such as an
Intel-based processor, IBM mainframe, server, or other type of
commercially available processor able to support incoming traffic
in accordance with each particular embodiment and application.
[0205] It should be noted that the particulars of the hardware and
processes included in each of the host systems 3214a-3214n, as well
as those components that may be included in the data storage system
3212 are described herein in more detail, and may vary with each
particular embodiment. Each of the host computers 3214a-3214n, as
well as the data storage system 3212, may all be located at the
same physical site, or, alternatively, may also be located in
different physical locations. Examples of the communication medium
that may be used to provide the different types of connections
between the host computer systems, the data manager system, and the
data storage system of the computer system 3210 may use a variety
of different communication protocols such as SCSI, ESCON, Fiber
Channel, or functional equivalents that are known to those skilled
in the computer modeling and simulation field. Some or all of the
connections by which the hosts and data storage system 3212 may be
connected to the communication medium 3218 may pass through other
communication devices, such as a Connectrix or other switching
equipment that may exist, both physical and virtual, such as a
phone line, a repeater, a multiplexer or even a satellite.
[0206] Each of the host computer systems may perform different
types of data operations, such as storing and retrieving data files
used in connection with an application executing on one or more of
the host computer systems. For example, a computer program may be
executing on the host computer 3214a and store and retrieve data
from the data storage system 3212. The data storage system 3212 may
include any number of a variety of different data storage devices,
such as disks, tapes, and the like in accordance with each
implementation. As will be described in following paragraphs,
methods may reside and be executing on any one of the host computer
systems 3214a-3214n. Data may be stored locally on the host system
executing the methods, as well as remotely in the data storage
system 3212 or on another host computer system. Similarly,
depending on the configuration of each computer system 3210, method
as described herein may be stored and executed on one of the host
computer systems and accessed remotely by a user on another
computer system using local data. A variety of different system
configurations and variations are possible then as will be
described in connection with the embodiment of the computer system
3210 of FIG. 32 and should not be construed as a limitation of the
techniques described elsewhere herein.
[0207] Referring now to FIG. 33, an exemplary aspect of a modeling
system 3319 is illustrated that may reside, for example, on a
single computer or in one of a plurality of host computer systems
(e.g., host computers 3214a-3214n). The modeling system may be
divided into several components. One exemplary aspect of the system
may include a GUI module 3320, a Modeling and Simulation module
3322, and a Data Storage and Retrieval module 3324. The GUI module
3320 can provide for interactions with system users. The Modeling
and Simulation module 3322 can provide an ability to manage and
perform a multiphysics simulation. The Data Storage and Retrieval
module 3324 can provide an ability to load and save the model in a
file, and to load and store other types of files which may be used
during the simulation or may be used as input or output to the
simulation.
[0208] The GUI module 3320 may communicate with the Modeling and
Simulation module 3322 by sending and receiving commands. The act
of sending and receiving commands may be performed through an
application programming interface ("API") or other similar
components. In one aspect of the system, the API may be object
oriented and mix data and function calls within the same structure.
In another aspect of the system, the API may use a data structure
that is separate from function calls.
[0209] It is contemplated that in certain aspects of the present
disclosure components of the multiphysics modeling system may
reside on different host computer systems. For example, the GUI
module 3320 may reside on a personal computer host and the Modeling
and Simulation module 3322 may reside on a server computer host. It
is further contemplated that the Data Storage and Retrieval module
3324 may reside on either the personal computer host or the server
computer host, or yet another separate computer host. If the
computer hosts are not identical, the API can be configured to use
a computer network to communicate between hosts. In one embodiment,
an object oriented API may be configured to send data and method
calls over the computer network or in another embodiment send data
and function calls between the components over a computer network.
The API may also be able to handle a Data Storage and Retrieval
module 3324 which may be located either on the host of the GUI
module 3320 or the Modeling and Simulation module 3322, or on a
separate host. In each of those cases, the Data Storage and
Retrieval module 3324 may be configured to load and store files on
each of those hosts.
[0210] It is contemplated that in certain aspects, the system 3319
may include, or be configured with, components other than what is
described and represented in the modeling system 3319 illustrated
in FIG. 33. In the exemplary aspect illustrated in FIG. 33,
Libraries 3326 and the User Data Files 3328 can be stored locally
within the host computer system. It is further contemplated that in
certain aspects, the Libraries 3326 and/or User Data Files 3328, as
well as copies of these, may be stored in another host computer
system and/or in the Data Storage System 3312 of the computer
system 3310. However, for simplicity and explanation in paragraphs
that follow, it may be assumed in a non-limiting manner that the
system 3319 may reside on a single host computer system such as
3214a with additional backups, for example, of the User Data Files
and Libraries, in the Data Storage System 3212.
[0211] In certain aspects of the present disclosure, portions of
the modeling system 3319, such as the GUI module 3320, the Modeling
and Simulation module 3322, the Data Storage and Retrieval module
3324, and/or the Libraries 3326 may be included or executed in
combination with commercially available systems. These components
may operate on one of the host systems 3214a-3214n, and may include
one or more operating systems, such as, Windows XP.RTM., Windows 7,
Windows HPC Server 2008 R2, Unix.RTM., Linux.RTM., or Mac OS. It is
further contemplated that the modules of the modeling system 3319
may written in any one of a variety of computer programming
languages, such as, C, C++, C#, Java.RTM., or any combination(s)
thereof, or other commercially available programming languages.
[0212] It is contemplated that the GUI module 3320 may display GUI
windows in connection with obtaining data for use in performing
modeling, simulation, and/or other problem solving for one or more
processes and/or physics phenomena under consideration by a system
user. The one or more processes and/or phenomena may be assembled
and solved by the Modeling and Simulation module 3322. That is,
user data may be gathered or received by the system using modules,
such as the GUI module 3320, and subsequently used by the Modeling
and Simulation module 3322. Thereafter, the data may be transferred
or forwarded to the Data Storage and Retrieval module 3324 where
the user-entered data may be stored in a separate data structure
(e.g., User Data Files 3328). It is contemplated that other data
and information may also be stored and retrieved from a separate
data structure, such as Libraries 3326, which may be used by the
Modeling and Simulation module 3322 or in connection with the GUI
module 3320.
[0213] The various data files that may be associated with a
modeling system, such as User Data Files 3328 and the Libraries
3326, may be stored in any one of a variety of data file formats in
connection with a file system used in the host computer system or
in the Data Storage System 3212. In certain aspects, the system
3319 may use any one of a variety of database packages in
connection with the storage and retrieval of data. The User Data
files 3328 may also be used in connection with other simulation and
modeling packages. For example, the User Data files 3328 may be
stored in a format that may also be used directly or indirectly as
an input to any one of a variety of other modeling packages. In
certain aspects, data may be imported and/or exported between the
multiphysics modeling system and another system. The format of the
data may be varied or customized in accordance with each of the
system(s) as well as in accordance with additional functionalities
that each of the system(s) may include.
[0214] It is contemplated that the systems and methods described
herein may be used for combining physics interfaces that model
different physical phenomena or processes. The combination of a
plurality of physics interfaces can be referred to as a
multiphysics model. Properties of the physics interfaces can be
represented by PDEs that may be automatically combined to form PDEs
describing physical quantities in a coupled system or
representation. The coupled PDEs may be displayed, for example, in
an "Equation view" that allows for the coupled PDEs to be modified
and used as input into a solver. It is also contemplated that the
PDEs may be provided to the solver either independently as one PDE
or a system of PDEs, describing a single phenomenon or process, or
as one or several systems of PDEs describing several phenomena or
processes.
[0215] In certain aspects of the present disclosure, a multiphysics
modeling system can provide an ability to combine physics
interfaces that model physical properties through one or more GUIs
that allow a user to select one or more physics interfaces from a
list. In addition to displaying physics interfaces names, it is
further contemplated that variable names for physical quantities
may be selected through a GUI. It is contemplated that the physics
interfaces may have different formulations that depend on a "Study"
settings feature, which is described in more detail elsewhere
herein.
[0216] It is further contemplated that it may be desirable for a
multiphysics modeling system to provide the ability to access
predefined combinations of several physics phenomena for defining
multiphysics model(s). The predefined combinations may be referred
to as multiphysics interfaces, which similar to the physics
interfaces, may also have different formulations that depend on a
study settings feature.
[0217] It is contemplated that in certain aspects of the present
disclosure physical properties can be used to model physical
quantities for component(s) and/or process(es) being examined using
the modeling system, and the physical properties can be defined
using a GUI that allow the physical properties to be described as
numerical values. In certain aspects, physical properties can also
be defined as mathematical expressions that include one or more
numerical values, space coordinates, time coordinates, and/or the
actual physical quantities. In certain aspects, the physical
properties may apply to some parts of a geometrical domain, and the
physical quantity itself may be undefined in the other parts of the
geometrical domain. A geometrical domain or "domain" may be
partitioned into disjoint subdomains. The mathematical union of
these subdomains forms the geometrical domain or "domain". The
complete boundary of a domain may also be divided into sections
referred to as "boundaries". Adjacent subdomains may have common
boundaries referred to as "borders". The complete boundary is the
mathematical union of all the boundaries including, for example,
subdomain borders. For example, in certain aspects, a geometrical
domain may be one-dimensional, two-dimensional, or
three-dimensional in a GUI. However, as described in more detail
elsewhere herein, the solvers may be able to handle any space
dimension. It is contemplated that through the use of GUIs in one
implementation, physical properties on a boundary of a domain may
be specified and used to derive the boundary conditions of the
PDEs.
[0218] Additional features of a modeling system, such as feature
that may be found in the Modeling and Simulation module 3322, may
provide for automatically deriving a system of PDE's and boundary
conditions for a multiphysics model. This technique can include
merging the PDEs of the plurality of phenomena or processes, and
may produce a single system of coupled PDEs, also using coupling
variables or operators to couple processes in different coordinate
systems, and may perform symbolic differentiation of the system of
PDEs with respect to all the dependent variables for later use by
the solver.
[0219] It is contemplated that in certain aspects, a coupled system
of PDEs may be modified before being differentiated and sent to the
solver. The modification may be performed using a settings window
included in a GUI displaying the combined PDEs in an "Equation
view". When the system of PDEs is modified in this way, the
settings for the corresponding physical properties can become
"locked". The properties may subsequently be unlocked by a user
taking certain action(s).
[0220] It is contemplated that certain aspects of the present
disclosure may include features for modeling one or more of a
plurality of engineering and scientific disciplines, including, for
example, acoustics, chemical reactions, diffusion,
electromagnetism, fluid dynamics, geophysics, heat transfer, porous
media flow, quantum mechanics, semiconductor devices, structural
mechanics, wave propagation, and the like. Certain aspects of a
modeling system may involve more than one of the foregoing
disciplines and can also include representing or modeling a
combination of the foregoing disciplines. Furthermore, the
techniques that are described herein may be used in connection with
one or more systems of PDEs.
[0221] It is contemplated that in certain aspects of the present
disclosure, system(s) of PDEs may be represented in general,
coefficient, and/or weak form. The coefficient form may be more
suitable in connection with linear or almost linear problems, while
the general and weak forms may be better suited for use in
connection with non-linear problems. The system(s) being modeled
may have one or more associated studies, for example, such as
stationary, time dependent, eigenvalue, or eigenfrequency. In the
aspects described herein, a finite element method (FEM) may be used
to solve for the PDEs together with, for example, adaptive meshing,
adaptive time stepping, and/or a choice of a one or more different
numerical solvers.
[0222] It is contemplated that in certain aspects of the present
disclosure, a finite element mesh may include simplices forming a
representation of a geometrical domain. Each simplex can belong to
a unique subdomain, and a union of the simplices can form an
approximation of the geometrical domain. The boundary of the domain
may also be represented by simplices of the dimensions 0, 1, and 2,
for geometrical dimensions 1, 2, and 3, respectively.
[0223] It is further contemplated that a mesh representing a
geometry may also be created by an outside or external application
and may subsequently be imported for use into the modeling
system(s) described in the present disclosure.
[0224] The initial value of the solution process may be given as
numerical values, or expressions that may include numerical values,
space coordinates, time coordinates and the actual physical
quantities. The initial value(s) may also include physical
quantities previously determined.
[0225] The solution of the PDEs may be determined for any portion
of the physical properties and their related quantities. Further,
any portion not solved for may be treated as initial values to the
system of PDEs.
[0226] It is contemplated that it may be desirable for a user to
select a space dimension, combinations of physics, and a type of
study in a multiphysics modeling system using a model wizard. The
model wizard may take the user through these selection steps and it
may also allow for the combination of several space dimensions,
several physics, and several studies or study steps in a
multiphysics model.
[0227] Each of these aspects and obvious variations thereof is
contemplated as falling within the spirit and scope of the claimed
invention, which is set forth in the following claims. Moreover,
the present concepts expressly include any and all combinations and
subcombinations of the preceding elements and aspects.
* * * * *