AbstractWhen solving multidimensional problems of gas dynamics, finite-volume schemes using complete (i.e., based on a three-wave configuration) solvers of the Riemann problem suffer from shock-wave instability. It can appear as oscillations that cannot be damped by slope limiters, or it can lead to a qualitatively incorrect solution (carbuncle effect). To combat instability, one can switch to incomplete solvers based on a two-wave configuration near the shock wave, or introduce artificial viscosity. The article compares these two approaches on unstructured grids in relation to the EBR-WENO scheme for approximating convective terms and the classical Galerkin method for approximating diffusion terms. It is shown that the method of introducing artificial viscosity usually makes it possible to more accurately reproduce the flow pattern behind the shock front. However, on a three-dimensional unstructured grid, it causes dips ahead of the front, the depth of which depends on the quality of the grid, which can lead to an emergency stop of the calculation. Switching to an incomplete solver in this case gives satisfactory results with a much lower sensitivity to the quality of the mesh.