Numerical resolution of well-balanced shallow water equations with complex source terms

Fabien Marche (1) , Qiuhua Liang (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 School of Civil Engineering and Geosciences [Newcastle]

This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile.

Domaines: Analyse numérique [math.NA]

Fabien Marche, Qiuhua Liang. Numerical resolution of well-balanced shallow water equations with complex source terms. Advances in Water Resources, 2009, 32 (6), pp.873))884. ⟨10.1016/j.advwatres.2009.02.010⟩. ⟨hal-00799080⟩