Robust finite volume schemes for 2D shallow water models. Application to flood plain dynamics

Frédéric Couderc (1) , Jerome Monnier (1, 2) , Jean-Paul Vila (2, 1) , Kévin Larnier (3) , Ronan Madec (1) , Denis Dartus (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 INSA - Institut National des Sciences Appliquées
3 IMFT - Institut de mécanique des fluides de Toulouse

This study proposes original combinations of higher order Godunov type finite volume schemes and time discretization schemes for the 2d shallow water equations, leading to fully second-order accuracy with well-balanced property. Also accuracy, positiveness and stability properties in presence of dynamic wet/dry fronts is demonstrated. The test cases are the classical ones plus extra new ones representing the geophysical flow features and difficulties.

Mots clés: finite volumes; Shallow water; second order; wet-dry front

Domaines: Analyse numérique [math.NA]

Frédéric Couderc, Jerome Monnier, Jean-Paul Vila, Kévin Larnier, Ronan Madec, et al.. Robust finite volume schemes for 2D shallow water models. Application to flood plain dynamics. 2015. ⟨hal-01133594⟩