Analysis of coupling methods: a review

Abstract

The multiphysics field is a branch of physics whose objective is to couple at least two physical systems. Each is governed by its own principles of evolution or equilibrium such as balance laws or constitutive laws. Many engineering problems can only be described correctly by coupling fields of physics that have historically been developed and taught separately. These problems require on the one hand a good understanding of each physical domain, but above all an analysis of the coupling mechanisms of these physical domains, in order to propose a relevant model capable of solving the problem. A challenge in the multiphysics (mechatronics) field is the construction of coupled multiphysics models from experimental observations, as well as the analysis of their mathematical properties. The mathematical analysis of the coupled model must be able to show the well-posedness of the problem at the defined boundary and initial values. For this reason, we have identified several coupling methods: Newton, Gauss-Seidel, JNFK, and direct and explicit coupling. From these methods, it appears that the Newton method is suitable for the coupling of the different disciplines of Mechatronics. A summary table shows the comparative advantages of each method.