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.
|Original language||English (US)|
|Journal||International Journal for Numerical Methods in Fluids|
|State||Published - Jan 29 2022|
Bibliographical noteKAUST Repository Item: Exported on 2022-02-01
Acknowledgements: We thank Prof. Friedemann Kemm for sharing helpful code with us and for reviewing an early version of this manuscript.
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Computational Mechanics
- Applied Mathematics
- Computer Science Applications