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

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. Snapshot of a chaotically deforming circular hydraulic jump, computed using a novel numerical method that avoids carbuncles without suppressing the instability of this flow. The central circle represents the inflow jet, and the white area around it is a region of high‐speed shallow flow. The plot shows the gradient of surface height on a logarithmic scale.