Coupling Methods For Heat-Transfer And Heat-Flow: Operator Splitting And Parareal

Juergen Geiser , Stefan Guettel

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 18 pp.

MSC 2000

65M15 Error bounds

65L05 Initial value problems

Abstract
In this paper, we propose an operator splitting method for coupling heat-transfer and heat-flow equations. The motivation arose of industrial software packages, which have developed independently heat-transfer solvers (e.g. Aura-Fluid software package) and heat-flow solvers (e.g. Openfoam). Such packages are often simple coupled by A-B splitting and they simulate the influence of solar heat in car bodies. One of the main problems is to accelerate the code by iterative operator splitting methods and with a parallel interfaces. We propose Parareal as well applicable for parallel method for parabolic problems and also a speedup to mixed parabolic and hyperbolic problems is possible and delicate. Our idea is to combine the splitting schemes as a time-splitting method to adapt the time steps with Parareal as a time-parallelization method. Our analysis of these new splitting techniques provides error estimates which are validated at certain benchmark problems.