Well-balanced central WENO schemes for the sediment transport model in shallow water

Abstract

Sediment transport model in shallow water admits steady-state solutions in which the non-zero flux gradient is exactly balanced by the source term. In this paper, we develop high-order well-balanced central weighted essentially non-oscillatory schemes for the sediment transport model. In order to maintain the well-balanced property, we first reformulate the governing equations by an equivalent form and propose a novel reconstruction procedure for the Runge-Kutta flux. Rigorous theoretical analysis as well as extensive numerical examples all suggest that the present schemes preserve the well-balanced property. Moreover, the resulting schemes keep genuine high-order accuracy for general solutions.