Simple demonstration of different types of coupling in multiphysics numerical problems

TL;DR

This paper presents a simple demonstrator for illustrating three common types of coupling in multiphysics numerical problems, aiding understanding and teaching of complex coupled phenomena.

Contribution

It introduces an accessible, hands-on tool using a nonlinear heat equation to demonstrate one-way, explicit sequential, and full coupling methods.

Findings

Effective visualization of coupling types

Enhanced understanding of multiphysics coupling

Practical teaching aid for complex models

Abstract

Numerical modelling of coupled multiphysics phenomena is becoming an increasingly important subject in applied mathematics. The main challenge in teaching this subject is the complexity of both the mathematical models and their numerical implementation. In this note, a simple demonstrator is proposed that enables demonstration of and some hands-on experience with three types of coupling commonly used in computational science: one-way coupling, explicit sequential coupling, and full coupling. It makes use of a familiar nonlinear heat equation in 1D, with the solution being a propagating heat wave.