A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation

TL;DR

This paper introduces a new multilayer Saint-Venant system with mass exchanges between layers, derived from Navier-Stokes equations, and validates it through numerical tests demonstrating its effectiveness in complex flow scenarios.

Contribution

The paper develops a novel multilayer shallow water model with mass exchanges, including derivation, theoretical properties, and numerical validation.

Findings

Model preserves positivity and energy properties.

Effective for recirculation flows with wind forcing.

Numerical tests confirm versatility and accuracy.

Abstract

The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighborhing layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.