A Numerical Method for the Two Layer Shallow Water Equations with Dry States

TL;DR

This paper introduces a high-resolution finite volume numerical method for two-layer shallow water equations with variable bathymetry, effectively handling dry states and complex wave interactions in one-dimensional models.

Contribution

It presents a novel numerical scheme based on f-wave-propagation that accurately manages dry states and variable bathymetry in two-layer shallow water systems.

Findings

Successfully models dry states in two-layer systems

Demonstrates accurate wave propagation in idealized ocean scenarios

Handles complex flux and source term interactions

Abstract

A numerical method is proposed for solving the two layer shallow water equations with variable bathymetry in one dimension based on high-resolution f-wave-propagation finite volume methods. The method splits the jump in the fluxes and source terms into waves propagating away from each grid cell interface. It addresses the required determination of the system's eigenstructure and a scheme for evaluating the flux and source terms. It also handles dry states in the system where the bottom layer depth becomes zero, utilizing existing methods for the single layer solution and handling single layer dry states that can exist independently. Sample results are shown illustrating the method and its handling of dry states including an idealized ocean setting.