An analytical solution of Shallow Water system coupled to Exner equation

TL;DR

This paper presents an exact analytical solution for the coupled shallow water and Exner sediment transport equations, providing benchmarks for validating numerical approximation methods in erosion modeling.

Contribution

It introduces a novel exact smooth solution applicable to common sedimentation laws, aiding in the validation of numerical methods for erosion simulations.

Findings

Provides a valid analytical benchmark for sediment transport models

Applicable to widely used sedimentation laws like Grass and Meyer-Peter & Muller

Facilitates validation of numerical approximation methods in erosion modeling

Abstract

In this paper, 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 & Muller. One of the main interest of this solution is the derivation of numerical benchmarks to valid the approximation methods.