A Simple Low-Dissipation Roe-Scheme Modification to Cure Shock Instabilities at High Mach Numbers

The grid-aligned shock instability limits an accurate simulation of Flow conditions involving high Mach number shock waves by state-of-the-art low-dissipation Riemann solvers. We propose a simple and efficient modification to the Roeux, which cures the shock instability and preserves the favorable low dissipation property of the approximate Riemann solver completely without the necessity of any additional detection procedure. When the shock front moves aligned to a Cartesian grid, which is the typical configuration of the instability, disturbances parallel to the shock occur with vanishing Mach number. We performed a series of numerical investigations that indicate that the incorrect scaling behavior of the numerical dissipation in transverse direction to the shock front is the prime reason for the shock instability. A simple modification reduces the acoustic contribution to the local dissipation for low Mach numbers. We obtained both stable and accurate results for test cases known to suffer from the carbuncle phenomenon or the odd-even decoupling phenomenon.     «

The grid-aligned shock instability limits an accurate simulation of Flow conditions involving high Mach number shock waves by state-of-the-art low-dissipation Riemann solvers. We propose a simple and efficient modification to the Roeux, which cures the shock instability and preserves the favorable low dissipation property of the approximate Riemann solver completely without the necessity of any additional detection procedure. When the shock front moves aligned to a Cartesian grid, which is the t...     »