A note on the carbuncle in shallow water simulations

TL;DR

This paper investigates the carbuncle phenomenon in shallow water simulations at high Froude numbers, demonstrating that solutions from gas dynamics can be adapted to mitigate this numerical instability.

Contribution

It extends the understanding of the carbuncle problem from gas dynamics to shallow water flows and suggests that existing cures are applicable.

Findings

Carbuncle occurs in shallow water simulations at high Froude numbers.

Existing gas dynamics remedies are effective in shallow water contexts.

Numerical evidence supports the transferability of mitigation techniques.

Abstract

An important problem in gas dynamics simulation is to prevent the carbuncle, a breakdown of discrete shock profiles. We show that for high Froude number, this also occurs in shallow water simulations and give numerical evidence that all cures developed for gas dynamics should also work in shallow water flows.