A well-balanced high-resolution shape-preserving central scheme to solve one-dimensional sediment transport equations

We present a well-balanced high-resolution non-oscillatory central finite volume scheme for solving the shallow water equations with a non-flat bottom topology. Time integration is obtained following a Runge-Kutta procedure, coupled with its natural continuous extension. We use a central scheme with a point value reconstruction algorithm based on average or flux values, which satisfies the monotonicity preserving property. We apply a special treatment for the source term spatial integration, which preserves the time and space accuracy and it results in a well-balanced scheme. Several one-dimensional test cases are used to verify the behaviour and non-oscillatory properties of our scheme.