A simple three-wave Approximate Riemann Solver for the Saint-Venant–Exner equations

Emmanuel Audusse (1, 2) , Christophe Chalons (3) , Philippe Ung (4, 2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 ANGE - Numerical Analysis, Geophysics and Ecology
3 LMV - Laboratoire de Mathématiques de Versailles
4 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

The Saint-Venant–Exner equations are widely used in the literature and industrial codes to model the bedload sediment transport. In industrial codes, the resolution of this system of equations is mostly approached by a splitting method which allows a weak coupling between the hydraulic and morphodynamic models but may suffer from stability issues. In recent works, many authors proposed alternative finite volume methods based on a strong coupling to cure this problem. This work pursues two objectives : first we propose a numerical scheme to approximate the solution of the coupled model with a Godunov-type method based on a three-wave Approximate Riemann Solver (ARS) and, second, we extend the purpose to exhibit what is the minimal coupling that ensures the stability of the global numerical process when dealing with collocated finite volume schemes.

Mots clés: shallow-water equations; Exner equation; splitting method; non-splitting method; approximate Riemann solver; finite volume method; positivity preserving; well-balanced scheme

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Emmanuel Audusse, Christophe Chalons, Philippe Ung. A simple three-wave Approximate Riemann Solver for the Saint-Venant–Exner equations. 2015. ⟨hal-01204754v1⟩