In
computational modelling
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be deter ...
, multiphysics simulation (often shortened to simply "multiphysics") is defined as the simultaneous simulation of different aspects of a physical system or systems and the interactions among them.
For example, simultaneous simulation of the physical stress on an object, the temperature distribution of the object and the thermal expansion which leads to the variation of the stress and temperature distributions would be considered a multiphysics simulation. Multiphysics simulation is related to multiscale simulation, which is the simultaneous simulation of a single process on either multiple time or distance scales.
As an
interdisciplinary
Interdisciplinarity or interdisciplinary studies involves the combination of multiple academic disciplines into one activity (e.g., a research project). It draws knowledge from several other fields like sociology, anthropology, psychology, ec ...
field, multiphysics simulation can span many science and engineering disciplines. Simulation methods frequently include
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
,
partial differential equations
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
and
tensor analysis.
Multiphysics simulation process
The implementation of a multiphysics simulation follows a typical series of steps:
* Identify the aspects of the system to be simulated, including physical processes, starting conditions, and the coupling or boundary conditions among these process.
* Create a
discrete
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
* Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
*Discrete group, a ...
mathematical model of the system.
*
Numerically
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
solve the model.
* Process the resulting data.
Mathematical models
Mathematical models used in multiphysics simulations are generally a set of coupled equations. The equations can be divided into three categories according to the nature and intended role:
governing equation The governing equations of a mathematical model describe how the values of the unknown variables (i.e. the dependent variables) change when one or more of the known (i.e. independent) variables change.
Mass balance
A mass balance, also called a ...
,
auxiliary equations and
boundary/initial conditions. A governing equation describes a major physical mechanisms or process. Multiphysics simulations are numerically implemented with
discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...
methods such as the
finite element method,
finite difference method, or
finite volume method.
Challenges of multiphysics simulation
Generally speaking, multiphysics simulation is much harder than that for individual aspects of the physical processes.
The main extra issue is how to integrate the multiple aspects of the processes with proper handling of the interactions among them.
Such issue becomes quite difficult when different types numerical methods are used for the simulations of individual physical aspects.
For example, when simulating a
fluid-structure interaction problem with typical Eulerian finite volume method for flow
and Lagrangian finite element method for structure dynamics.
See also
*
Finite difference time-domain method
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis technique used for modeling computational electrodynamics (finding approximate solutions to ...
References
*
Susan L. Graham
Susan Lois Graham (born September 16, 1942) is an American computer scientist. Graham is the Pehong Chen Distinguished Professor Emerita in the Computer Science Division of the Department of Electrical Engineering and Computer Sciences at the U ...
, Marc Snir, and Cynthia A. Patterson (Editors), ''Getting Up to Speed: The Future of Supercomputing,'
Appendix D The National Academies Press, Washington DC, 2004. {{ISBN, 0-309-09502-6.
* Paul Lethbridge, ''Multiphysics Analysis'', p26, The Industrial Physicist, Dec 2004/Jan 2005
Archived at
Numerical analysis
Computational physics