Simple demonstration of different types of coupling in multiphysics numerical problems

Abstract

Numerical modelling of coupled multiphysics phenomena is becoming an increasingly important subject in computational physics and computational mechanics. The main challenge in teaching this subject is the complexity of both the mathematical models and their numerical implementations. In this contribution, a toy numerical model is used to demonstrate three types of coupling commonly used in computational science: one-way coupling, explicit sequential coupling and full coupling. It makes use of a nonlinear heat equation in 1D, with the solution being a propagating heat wave. Experimental convergence analysis demonstrates that the results obtained with sequential coupling approach those obtained with full coupling as the timestep is reduced. The example developed in this contribution can be used in the courses on numerical modelling or computational science & engineering offered to engineering students.