CFL-less Discontinuous Galerkin solver

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

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

We describe an explicit Discontinuous Galerkin (DG) kinetic scheme for solving systems of conservation laws. The solver is stable for an arbitrary CFL number and has the complexity of an explicit scheme. It can be applied to any hyperbolic system of conservation laws. In this work we assess the performance of the scheme in the particular case of the three-dimensional wave equation and of Maxwell's equations. We measure the benefit of the CFL-less feature and the parallel possibilities of the method.

Mots clés: Discontinuous Galerkin; kinetic approximation; CFL-less

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Pierre Gerhard, Philippe Helluy, Victor Michel-Dansac. CFL-less Discontinuous Galerkin solver. 2021. ⟨hal-03218086v1⟩