Steady States and Well-balanced Schemes for Shallow Water Moment Equations with Topography

TL;DR

This paper develops a new hyperbolic shallow water moment model incorporating topography, identifies its steady states, and introduces a well-balanced scheme to accurately preserve these states in simulations.

Contribution

It presents a novel hyperbolic shallow water moment model based on linearized equations and a tailored well-balanced numerical scheme for steady state preservation.

Findings

Model is hyperbolic and well-balanced.

Steady states are fully characterized.

Numerical scheme preserves steady states effectively.

Abstract

In this paper, we investigate steady states of shallow water moment equations including bottom topographies. We derive a new hyperbolic shallow water moment model based on linearized moment equations that allows for a simple assessment of the steady states. After proving hyperbolicity of the new model, the steady states are fully identified. A well-balanced scheme is adopted to the specific structure of the new model and allows to preserve the steady states in numerical simulations.