Cell-vertex entropy-stable finite volume methods for the system of Euler equations on unstructured grids

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

“…For this particular problem, using method ( 7) with the blended Riemann solver leads to 𝜆 min i±1∕2 = 0 for all the experiments. We can artificially activate the entropy stabilization by imposing 𝜃 i = 0 in (17), which is equivalent to using Roe's solver with extra dissipation given by 𝜆 min i±1∕2 . In Figure 1D we show the solution, and in the last column of Table 1 we summarize the results of a convergence test.…”

“…By doing this, our blended solver induces dissipation of entropy. Entropy dissipative Riemann solvers have been used to produce carbuncle free solvers for the Euler equations; see for instance 6,16,17 . However, to the best of our knowledge, this idea has not been used before to suppress carbuncle instabilities for the shallow water equations.…”