Combined characteristics and finite volume methods for sediment transport and bed morphology in surface water flows

Authors:
Fayssal Benkhaldoun;Mohammed Seaïd
Affiliations:
LAGA, Université Paris 13, 99 Av J.B. Clement, 93430 Villetaneuse, Paris, France;School of Engineering and Computing Sciences, University of Durham, South Road, DH1 3LE, UK
Venue:
Mathematics and Computers in Simulation
Year:
2011

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Abstract

Abstract: We propose a new numerical method for solving the equations of coupled sediment transport and bed morphology by free-surface water flows. The mathematical formulation of these models consists of the shallow water equations for the hydraulics, an advection equation for the transport of sediment species, and an Exner equation for the bedload transport. The coupled problem forms a one-dimensional hyperbolic system of conservation laws with geometric source terms. The proposed numerical method combines the method of characteristics with a finite volume discretization of the system. The combined method is simple to implement and accurately resolves the governing equations without relying on Riemann problem solvers. Numerical results are presented for several test examples on sediment transport and bed morphology by free-surface water flows.