Parallel kinetic schemes for conservation laws, with large time steps

Pierre Gerhard, Philippe Helluy, Victor Michel-Dansac, Bruno Weber

Published 2022-12-21Version 1

We propose a new parallel Discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not require the assembly and resolution of large linear systems for the time iterations. The approach is based on a kinetic representation of the system of conservation laws previously investigated by the authors. In this paper, the approach is extended with a subdomain strategy that improves the parallel scaling of the method on computers with distributed memory.