On using artificial viscosity in edge-based schemes on unstructured meshes

In numerical simulation of multidimensional gas dynamics, finite-volume schemes based on complete (i.e. based on three-wave model) Riemann solvers suffer from shock-wave instability. It can appear as oscillations that cannot be damped by slope limiters, or it can lead to a non-physical solution (carbuncle-phenomenon). To overcome this, one can switch to an incomplete (i.e. based on two-wave model) Riemann solver or introduce artificial viscosity. We compare these two approaches as applied to the EBR-WENO scheme for the discretization of convective fluxes and for the continuous P1-Galerkin method for the discretization of diffusion terms. We show that the results of simulations are more accurate if the method of artificial viscosity is used. However, on 3D unstructured meshes this way causes pressure pimples on the supersonic side of the shock, the amplitudes of which depend on the mesh quality. They can reach negative pressure and thus can result in crash of time integration. In this case, the switch to an incomplete Riemann solver gives satisfactory results with much less sensitivity to the quality of the mesh.