Barrier Simulations with Shallow Water Equations using the State Redistribution Method

TL;DR

This paper introduces a state redistribution method for shallow water equations to efficiently simulate small-scale barriers in coastal flooding, reducing computational time while maintaining accuracy.

Contribution

The paper presents a novel application of the state redistribution method to shallow water equations, improving simulation efficiency and ease of implementation for barrier modeling.

Findings

Reduces computational time fivefold compared to adaptive refinement.

Maintains conservation and geometric simplicity in simulations.

Demonstrates convergence and effectiveness against other methods.

Abstract

The representation of small scale barriers, such as sea-walls, in coastal flooding simulations is a common computational constraint that can be difficult to overcome due to the combination of the need for resolution and the CFL constraining time stepping involved in solving the underlying PDE. This article proposes an approach that uses the state redistribution method (SRD) on shallow water equations to alleviate these problems while remaining conservative and geometrically easy to implement. We will demonstrate the method versus two other comparable approaches along with convergence results. In particular, we save computational time by reducing time steps fivefold when compared to simulation with same resolution using adaptive refinement at the barrier.