Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump

TL;DR

This paper introduces a new Riemann solver based on entropy residuals to prevent carbuncle artifacts in shallow water simulations, successfully balancing accuracy and stability in modeling hydraulic jumps.

Contribution

A novel entropy-based Riemann solver that effectively prevents carbuncle artifacts without suppressing physical hydraulic jump instabilities.

Findings

The new solver avoids carbuncles while preserving physical instabilities.

Existing cures either suppress instabilities or produce carbuncles.

The proposed method maintains high accuracy in shallow water simulations.

Abstract

We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while maintaining high accuracy. We propose a new challenging test problem for shallow water codes, consisting of a steady circular hydraulic jump that can be physically unstable. We show that numerical methods are prone to either suppress the instability completely or form carbuncles. We test existing cures for the carbuncle. In our experiments, only the proposed method is able to avoid unphysical carbuncles without suppressing the physical instability.