Shallow water equations for large bathymetry variations

TL;DR

This paper introduces an enhanced nonlinear shallow water model that accounts for significant seabed variations, derived from a variational principle without relying on small parameters, improving accuracy in complex bathymetric conditions.

Contribution

The paper presents a novel shallow water model explicitly incorporating large bathymetry variations, derived variationally without small parameter assumptions.

Findings

Model effectively captures effects of large seabed variations.

Derivation method is general and does not depend on small parameters.

Potential for improved simulation accuracy in complex terrains.

Abstract

In this study, we propose an improved version of the nonlinear shallow water (or Saint-Venant) equations. This new model is designed to take into account the effects resulting from the large spacial and/or temporal variations of the seabed. The model is derived from a variational principle by choosing the appropriate shallow water ansatz and imposing suitable constraints. Thus, the derivation procedure does not explicitly involve any small parameter.