A well-balanced Runge--Kutta Discontinuous Galerkin method for the Shallow-Water Equations with flooding and drying

Alexandre Ern (1) , Serge Piperno (1) , Karim Djadel (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

We build and analyze a Runge--Kutta Discontinuous Galerkin method to approximate the one- and two-dimensional Shallow-Water Equations. We introduce a flux modification technique to derive a well-balanced scheme preserving steady-states at rest with variable bathymetry and a slope modification technique to deal satisfactorily with flooding and drying. Numerical results illustrating the performance of the proposed scheme are presented.

Mots clés: Runge--Kutta Discontinuous Galerkin; Shallow-Water Equations; source terms; well-balanced schemes; flooding and drying

Domaines: Analyse numérique [math.NA]

Alexandre Ern, Serge Piperno, Karim Djadel. A well-balanced Runge--Kutta Discontinuous Galerkin method for the Shallow-Water Equations with flooding and drying. 2007. ⟨hal-00153788⟩