Analysis of the Effects of Curvature on the Solutions of Shallow Water Equations

TL;DR

This paper compares standard and extended shallow water models to assess how surface curvature affects solutions, finding the standard model remains a good approximation in many practical cases.

Contribution

It introduces an extended model accounting for surface curvature and compares its solutions to the standard model across various base flow surfaces.

Findings

Standard model approximates extended model well in many cases

Curvature effects are significant for certain flow configurations

Extended model provides more accurate solutions when curvature varies greatly

Abstract

The most used form of the Shallow Water Equations doesn't take into account the variation of the curvature of the base flow surface. In this paper, we compare the theoretical and numerical solutions of the standard model and with the solutions of an extended model and for a large class of base flow surfaces. We find that the solution of the standard model is still a good approximation for the extended model for many real life applications.