Gregor Gassner, Department of Mathematics and Computer Science, University of Cologne
Manuel Torrilhon, Applied and Computational Mathematics, RWTH Aachen
Main Collaborator in the Research Unit:
Michael Schlottke-Lakemper, High-Performance Computing Center Stuttgart, University of Stuttgart
The overall research objective of this project is to address the different time scales that are present in adaptive multi-scale and multi-physics simulations. In particular, the project focuses on alleviating the temporal stiffness induced by, e.g., vastly different grid cell sizes during an adaptive multi-scale simulation, and/or the stiffness introduced by vastly varying wave speeds in the physical model. Vastly different time scales may for instance be present when coupling several different physical models. The general strategy is to consider several existing approaches, such as explicit many-stage RK schemes, Paired RK methods, IMEX RK schemes and the idea of optimized coefficients to maximize the time step stability for a given spatial operator and combine them in a unique creative way, to craft a novel time integration methodology. The highlight of the proposed methodology is that by construction, different explicit and implicit RK methods with varying number of derivative evaluations can be seamlessly coupled and thus, the entire simulation operates always at a synchronous common time level (typically the current RK stage time) while still fully accounting for the local multi-scale stiffness and multi-physics behaviour.