Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Embargo End Date2023-01-29
Permanent link to this recordhttp://hdl.handle.net/10754/668182
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AbstractWe 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.
CitationKetcheson, D. I., & Quezada de Luna, M. (2022). Numerical simulation and entropy dissipative cure of the carbuncle instability for the shallow water circular hydraulic jump. International Journal for Numerical Methods in Fluids. doi:10.1002/fld.5070
SponsorsWe thank Prof. Friedemann Kemm for sharing helpful code with us and for reviewing an early version of this manuscript.