Shallow Water Moment models for bedload transport problems

TL;DR

This paper introduces a shallow water moment model for bedload sediment transport that captures the vertical flow structure, improving the accuracy of sediment velocity approximation near the bed.

Contribution

It develops a novel shallow water Exner moment model with polynomial velocity profiles and an adapted IFCP scheme for better sediment transport simulation.

Findings

Enhanced vertical flow structure representation

Improved approximation of sediment velocity near the bed

Effective numerical scheme for large and short time scales

Abstract

In this work a simple but accurate shallow model for bedload sediment transport is proposed. The model is based on applying the moment approach to the Shallow Water Exner model, making it possible to recover the vertical structure of the flow. This approach allows us to obtain a better approximation of the fluid velocity close to the bottom, which is the relevant velocity for the sediment transport. A general Shallow Water Exner moment model allowing for polynomial velocity profiles of arbitrary order is obtained. A regularization ensures hyperbolicity and easy computation of the eigenvalues. The system is solved by means of an adapted IFCP scheme proposed here. The improvement of this IFCP type scheme is based on the approximation of the eigenvalue associated to the sediment transport. Numerical tests are presented which deal with large and short time scales. The proposed model allows to obtain the vertical structure of the fluid, which results in a better description on the bedload transport of the sediment layer.