Multiphysics

Multiphysics is the study and simulation of systems in which two or more physical processes interact and influence each other. Examples include fluid flow coupled with structural deformation, heat transfer coupled with electrical fields, and chemical reactions that alter material properties. Real-world problems often involve fields that span different spatial and temporal scales, requiring a unified mathematical model that combines the governing equations of the participating physics, along with appropriate constitutive relations and boundary conditions.

Modeling approaches to multiphysics fall into monolithic and partitioned strategies. In monolithic formulations, all governing equations are assembled into a single coupled system and solved simultaneously. Partitioned (or loosely coupled) methods solve subproblems for each physics separately and exchange information at interfaces iteratively. The couplings can be strong, with substantial mutual influence, or weak, where interaction occurs mainly through boundary data. Nonlinearities and stiff couplings pose additional numerical challenges.

Numerical methods for multiphysics typically employ discretization techniques such as finite element, finite volume, or finite difference methods, with time integration using implicit, explicit, or multirate schemes. Achieving stability and convergence of the coupled system, handling non-matching meshes, and controlling computational cost are common concerns. Verification and validation are important due to the increased model complexity and data requirements.

Applications span engineering, physics, and biology, including aeroelasticity, thermo-mechanical analysis, electro-thermal devices, magnetohydrodynamics, battery and fuel-cell modeling, cardiovascular mechanics, and geophysical simulations. Many general-purpose simulation environments and libraries provide built-in multiphysics capabilities, enabling integrated simulations across multiple disciplines.