Methods for suppressing carbuncle phenomenon based on various Riemann problem solvers

Carbuncle phenomenon is a numerical instability that manifests itself in problems with strong shock waves in the form of sawtooth perturbations of the shock wave front, a tumor-like growth on the shock wave, or its non–physical bending. The aim of the work is to compare methods of suppressing carbuncle phenomenon based on various Riemann problem solvers and to identify the most effective of them. To achieve this goal, were considered the main methods of combating carbuncle, was chosen a method for comparing carbuncle suppression methods, and the selected methods were applied to the test task. The problem of the interaction of a shock wave with a vortex was chosen as a test problem. Two types of errors have been identified: startup-errors and carbuncle. To eliminate the first type of errors, it is recommended to use the methods of Godunov, Roe, HLLE and HLLEC (and their modifications). The HLLEs (dissipative solver) and Rotated Riemann Solver (RRS) approaches were used to eliminate the second type of error. When comparing these approaches, the best result in terms of calculation accuracy was shown by the RRS method using the HLLEsC solver calculating the flow normal to the physical gap and the HLLEs solver calculating the flow along the gap.