Quasi-explicit, unconditionally stable, discontinuous galerkin solvers for conservation laws

Philippe Helluy (1, 2) , Pierre Gerhard (1, 2) , Victor Michel-Dansac (2) , Bruno Weber (3)

1 IRMA - Institut de Recherche Mathématique Avancée
2 TONUS - TOkamaks and NUmerical Simulations
3 AxesSim

We have developed in a previous work a parallel and quasi-explicit Discontinuous Galerkin (DG) kinetic scheme for solving hyperbolic systems of conservation laws. The solver is unconditionally stable (i.e., the CFL number can be arbitrary), has the complexity of an explicit scheme. It can be applied to any hyperbolic system of balance laws. In this work, we improve the parallel scaling of the method thanks to an implicit-explicit subdomain decomposition strategy.

Domains: Analysis of PDEs [math.AP]

Philippe Helluy, Pierre Gerhard, Victor Michel-Dansac, Bruno Weber. Quasi-explicit, unconditionally stable, discontinuous galerkin solvers for conservation laws. [Research Report] IRMA (UMR 7501). 2022. ⟨hal-03665248⟩