A well-balanced Discontinuous-Galerkin Lagrange-Projection scheme for the Shallow Water Equations

Christophe Chalons (1) , Maxime Stauffert (1, 2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 MDLS - Maison de la Simulation

This work considers the Shallow Water equations (SWE) and proposes a high order conservative scheme based on a Lagrange-Projection decomposition. The high order in space and time are achieved using Discontinuous-Galerkin (DG) and Runge-Kutta (RK) strategies. The use of a Lagrange-Projection decomposition enables the use of time steps that are not constrained by the sound speed thanks to an implicit treatment of the acoustic waves (Lagrange step), while the transport waves (Projection step) are treated explicitly. We prove that our scheme satisfies the well-balanced property as well as non linear stability properties. Numerical evidences are also given.

Mots clés: implicit explicit; large time steps; Lagrange-Projection decomposition; Shallow Water Equations; well-balanced property; high order discontinuous Galerkin schemes

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Christophe Chalons, Maxime Stauffert. A well-balanced Discontinuous-Galerkin Lagrange-Projection scheme for the Shallow Water Equations. 2017. ⟨hal-01612292⟩