An analytical solution of the shallow water system coupled to the Exner equation

Abstract

In this Note, an exact smooth solution for the equations modeling the bedload transport of sediment in shallow water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of Meyer-Peter and Müller. One of the main interests of this solution is the derivation of numerical benchmarks to valid the approximation methods.