US 7,623,991 B1 · Method and apparatus for the specification and automatic derivation of partial differential equations associated with coupled physical quantities in a multiphysics problem

Abstract

Disclosed is a system for representing and modeling one or more systems in which each system corresponds to an application mode. For each application mode, physical quantities are modeled and may be defined using a graphical user interface. Physical properties may be used to model the physical quantities of each system. The physical properties may be defined in terms of numerical values or constants, and mathematical expressions that may include numerical values, space coordinates, time coordinates, and actual physical quantities. Physical quantities and any associated variables may apply to some or all of a geometric domain, and may also be disabled in other parts of a geometrical domain. Partial differential equations describe the physical quantities. One or more application modes may be combined using an automated technique into a combined system of partial differential equations as a multiphysics model. A portion of the physical quantities and variables associated with the combined system may be selectively solved for. The partial differential equations may be displayed and may in turn solve for the system of partial differential equations in accordance with a general form or a coefficient form. An automated technique provides for automatic derivation of the combined partial differential equations and boundary conditions. This technique automatically merges the equations from a plurality of application modes, and in some instances, performs symbolic differentiation of the equations, producing a single system of partial differential equations. A subset of physical quantities and associated variables not solved for may be used as initial values to the system of partial differential equations.

Claims115

Dependent claims

A method executed in a computer system with at least one physical computing device for producing a model of a combined physical system having physical quantities by representing physical quantities of said combined physical system in terms of a combined set of partial differential equations, said method comprising:

representing at least one of a plurality of physical systems as two or more selected application modes modeling physical quantities of said at least one of said plurality of physical systems, wherein said application modes are configured to model the physical quantities for at least one of structural mechanics properties, fluid dynamic properties, electromagnetic properties, chemical reaction properties, acoustic properties, and heat transfer properties of said physical system;
using a first physical computing device, determining a set of partial differential equations for each of said two or more selected application modes, parameters of said partial differential equations being physical quantities of corresponding ones of said plurality of physical systems;
using said first physical computing device or a second physical computing device, forming said combined set of partial differential equations using said determined sets of partial differential equations associated with said one of said plurality of physical systems;
and
outputting to a display device or a communication device said model of said combined physical system based on said combined set of partial differential equations for said two or more selected application modes for said one of said plurality of physical systems, whereby said model represents a mathematical expression of said physical quantities of said combined physical system.

2 more elements

An apparatus for producing a model of a combined physical system having physical quantities by representing physical quantities of said combined physical system in terms of a combined set of partial differential equations, said apparatus comprising:

a computer comprising a processor, a user input device, a display device, and a memory device, said memory device containing executable instructions for producing said model of said combined physical system having physical quantities by representing physical quantities of said combined physical system in terms of said combined set of partial differential equations, said executable instructions causing said processor to perform, upon execution, acts comprising
representing in up to three space dimensions at least one of a plurality of systems as two or more selected application modes modeling physical quantities of said one of said plurality of systems;
using said processor, determining a set of partial differential equations for each of said two or more selected application modes, parameters of said partial differential equations being physical quantities of corresponding ones of said plurality of systems;
forming said combined set of partial differential equations using sets of partial differential equations associated with said one of said plurality of systems;
and
outputting said model of said combined physical system to said display device or a communication device, said model based on said combined set of partial differential equations for said two or more selected application modes for said one of said plurality of systems, whereby said model represents a mathematical expression of said physical quantities of said combined physical system.

3 more elements

An apparatus for producing a model of a combined physical system having physical quantities by representing physical quantities of said combined physical system in terms of solving a system of partial differential equations, said apparatus comprising:

a computer system comprising a processor, a user input device, a display device, and a memory device, said memory device containing executable instructions for producing said model of said combined physical system having physical quantities by representing physical quantities of said combined physical system in terms of solving a system of partial differential equations, said executable instructions causing said processor to perform, upon execution, acts comprising
defining a plurality of user-defined application modes modeling physical quantities of an associated model;
selecting two or more of said user-defined application modes;
using said processor or another processor, determining sets of partial differential equations for said selected two or more user-defined application modes of said associated model, parameters of said partial differential equations being physical quantities of corresponding systems;
and
outputting to at least one of said display device, another memory device, and a communication device said model based on a combination of said determined sets of partial differential equations for said two or more selected user-defined application modes for said associated model, whereby said model represents a mathematical expression of said physical quantities of said combined physical system.

3 more elements

A method executed in a computer system with at least one physical computing device for producing a model of a combined physical system having physical quantities and a solution to said model, said method comprising:

representing said combined physical system by a geometry described by a mesh and a set of physical properties, said mesh including a plurality of elements, each of said elements being characterized by a shape;
providing a plurality of application modes;
selecting at least a first and a second of said application modes;
using a first physical computing device to generate a first plurality of partial differential equations based on said first application mode and a second plurality of partial differential equations based on said second application mode, each of the partial differential equations representing a behavior of at least one of said physical quantities of said model in response to said set of physical properties;
using said first physical computing device or a second physical computing device and the first and second pluralities of partial differential equations to form a combined system of partial differential equations;
generating a solution using said combined system of partial differential equations, said solution comprising numerical values for said physical quantities of node points in said mesh;
and
storing in a computer readable memory or in a computer readable data storage system said solution to said model.

5 more elements

Dependencies are inferred from the claim text.

Method and apparatus for the specification and automatic derivation of partial differential equations associated with coupled physical quantities in a multiphysics problem

Life of this patent

Method and apparatus for the specification and automatic derivation of partial differential equations associated with coupled physical quantities in a multiphysics problem

Life of this patent

Abstract

Claims115