A robust and well-balanced scheme for the 2D Saint-Venant system on unstructured meshes with friction source term

A Duran (1, 2, 3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LEMON - Littoral, Environment: MOdels and Numerics
3 IMAG - Institut Montpelliérain Alexander Grothendieck

In the following lines we propose a numerical scheme for the shallow water system supplemented by topography and friction source terms, in a 2d unstructured context. This work proposes an improved version of the well-balanced and robust numerical model recently introduced in [J. Comp. Phys., 235, 565–586, 2013] for the pre-balanced Shallow Water Equations, accounting for varying topography. The present work aims at relaxing the robustness condition and include a friction term. To this purpose, the scheme is modified using a recent method, entirely based on a modified Riemann solver. This approach preserves the robustness and well-balanced properties of the original scheme, and prevents from unstable computations in the presence of low water depths. A series of numerical experiments is devoted to highlight the performances of the resulting scheme. Simulations involving dry areas, complex geometry and topography are proposed to validate the stability of the numerical model in the neighbourhood of wet/dry transitions.

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

A Duran. A robust and well-balanced scheme for the 2D Saint-Venant system on unstructured meshes with friction source term. International Journal for Numerical Methods in Fluids, 2015, 78 (2), pp.89-121. ⟨10.1002/fld.4011⟩. ⟨hal-01121264⟩