Coupling methods for heat transfer and heat flow: Operator splitting and the parareal algorithm

We propose an operator splitting method for coupling heat transfer and heat flow equations. This work is motivated by the need to couple independent industrial heat transfer solvers (e.g., the Aura-Fluid software package) and heat flow solvers (e.g., Openfoam). Such packages are often used to simulate the influence of solar heat in car bodies and are coupled by A-B splitting techniques. The main goal of this work is the acceleration of the coupled software system by iterative operator splitting methods and additional time-parallelism using the parareal algorithm. We present these new splitting techniques along with some novel convergence results and test the splitting-parareal combination on various numerical problems.