Numerical errors generated in simulations of slowly moving shocks

An accurate treatment of shockwaves is critical in computational fluid dynamics ap-plications, because numerical errors may propagate in the flow field and contaminate the solution. Because of its simplicity and robustness, shock capturing has become over the past decades the most common means for simulating flows with shockwaves in a sta-ble fashion. However, an important drawback of many commonly used shock-capturing schemes is the generation of errors in computations of slowly moving shocks. Such errors may be particularly detrimental in problems in which small fluctuations interact with shockwaves, e.g., in aero-acoustics or turbulence. This problem was first identified by Woodward & Colella (1984) and studied system-atically by Roberts (1990). Depending on the shock speed relative to the grid and on the numerical scheme, errors and oscillations may occur and affect the solution. Jin & Liu (1996) provided an explanation for the occurrence of start-up errors with the Lax