7 problems

Approximate Riemann solvers use numerical mass fluxes, and a pressure jump term is a term in that flux proportional to a pressure jump. Liou's conjecture. Schemes that suffer from…

Consider Thornber et al.'s low-Mach modification of reconstructed interface velocities in Godunov-type schemes, in which the velocity difference is reduced as the Mach number decre…

The HLLCM and HLLEC schemes are approximate Riemann solvers, and a shear velocity perturbation is a perturbation in the velocity component tangential to the shock or grid-aligned n…

Consider a grid-aligned normal shock and perturbations in the plane transverse to its normal. Let $M_*$ denote the Mach number, and let low Mach corrections be modifications of app…

An upwind numerical scheme is strictly stable when its perturbations decay rather than merely remaining bounded, and it exactly resolves contact discontinuities when those disconti…

Robustness conjecture. The documented differences in robustness are due to the presence of both small-scale under-resolved features and significant variations in the density.

Dissipation-balancing conjecture. Choosing a seemingly less dissipative convection term is simply counterbalanced by other numerical dissipation mechanisms.