A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

Minh-Hoang Le (1, 2) , Stéphane Cordier (1) , Carine Lucas (1) , Olivier Cerdan (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)

Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe’s solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and twodimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

Mots clés: particle-size selectivity; Hairsine-Rose model; CFL conditon; positivity; shallow water equations; sedimentation; soil erosion; numerical stability; finite volume method; well-balanced scheme

Domaines: Modélisation et simulation; Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Sciences de la Terre

Minh-Hoang Le, Stéphane Cordier, Carine Lucas, Olivier Cerdan. A faster numerical scheme for a coupled system modeling soil erosion and sediment transport. Water Resources Research, 2015, 51 (2), pp.987-1005. ⟨10.1002/2014WR015690⟩. ⟨hal-00957667v2⟩