Simple demonstration of different types of coupling in multiphysics numerical problems

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.