A VFRoe scheme for 1D shallow water flows : wetting and drying simulation

TL;DR

This paper introduces a novel finite-volume scheme for 1D shallow water equations that effectively handles wetting and drying phenomena by preserving positivity through a specialized Riemann solver.

Contribution

It proposes a new VFRoe scheme with a celerity-speed formulation and an original approach to include topography, enabling accurate wetting and drying simulations.

Findings

Successfully simulates wetting and drying flows.

Preserves positivity of celerity in numerical solutions.

Demonstrates effectiveness through numerical test cases.

Abstract

A finite-volume method for the one-dimensional shallow-water equations including topographic source terms is presented. Exploiting an original idea by Leroux, the system of partial-differential equations is completed by a trivial equation for the bathymetry. By applying a change of variable, the system is given a celerity-speed formulation, and linearized. As a result, an approximate Riemann solver preserving the positivity of the celerity can be constructed, permitting wetting and drying flow simulations to be performed. Finally, the simulation of numerical test cases is presented.