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Multiphysics is a computational discipline which treats simulations that involve multiple physical models or multiple simultaneous physical phenomena. Examples include combining chemical kinetics and fluid mechanics and combining finite elements with molecular dynamics. Multiphysics typically involves solving coupled systems of partial differential equations.

Many physical simulations involve coupled systems, such as electric and magnetic fields for electromagnetism, pressure and velocity for sound, or the real and the imaginary part of the quantum mechanical wave function. Another case is the mean field approximation for the electronic structure of atoms, where the electric field and the electron wave functions are coupled.

Single discretization method[edit]

These software packages mainly rely on the finite element method or similar commonplace numerical methods for simulating coupled physics: thermal stress, electro- and acousto- magnetomechanical interaction[1], fluid structure interaction (FSI), fluid flow with heat transport and chemical reactions, electromagnetic fluids (magnetohydrodynamics or plasma), and electromagnetically induced heating. In many cases, to get accurate results, it is important to include mutual dependencies where the material properties significant for one field (such as the electric field) vary with the value of another field (such as temperature) and vice versa.

Multiple discretization methods[edit]

There are cases where each subset of partial differential equations has different mathematical behavior, for example when compressible fluid flow is coupled with structural analysis or heat transfer. To perform an optimal simulation in those cases, a different discretization procedure must be applied to each subset. For example, the compressible flow is discretized with a finite volume method and the conjugate heat transfer with a finite element analysis. Another example is the use of electromagnetic or electrostatic Particle-in-cell (PIC, EMPIC, ESPIC) methods combined with Direct simulation Monte Carlo, where the particles may interact with an electromagnetic (EM) field or other fields, with each other, and with fluids evolved by finite volume or other methods. The particles interact with the EM fields through the charges and currents they create and by being accelerated by the EM field. Particles collide with each other, and they collide with fluids.


  1. ^ S. Bagwell, P.D. Ledger, A.J. Gil, M. Mallett, M. Kruip, A linearised hp–finite element framework for acousto-magneto-mechanical coupling in axisymmetric MRI scanners, DOI: 10.1002/nme.5559
  • Susan L. Graham, 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, [1], Archived at: [2]