How to Do Multiphysics

Abstract

This chapter is intended to give out a general but definite answer to the question: “How to do multiphysics?” First, the essential sequential components of the implementation of multiphysics will be introduced: identifying a multiphysical process/system, developing a mathematical description of this process/system, discretizing this mathematical model into an algebraic system, and solving this algebraic equation system and postprocessing the data to obtain information of interest. Emphasis will be placed on both the abstraction of a multiphysical problem from a complex phenomenon with physical and mathematical languages, which is critical to the success of multiphysics analysis. This requires describing or modeling the system to be analyzed, including geometry, materials, and dominant physical mechanisms, using mathematical languages (function, tensor, differential equation) as computational domain, boundary conditions, auxiliary equations, and governing equations. Finally, the discretization, solution, and postprocessing using computers will be explained. The understanding underneath the above introduction is that multiphysics can be viewed as an art of physics, mathematics, applications, and numerical analysis.