An improved shock wave capturing method in high Mach numbers

Abstract

This study describes an improved scheme that can suppress numerical instabilities caused by calculating strong shock waves at high Mach numbers. The current scheme combines a clear detection of shock waves based on a sonic point condition with a hybrid numerical flux used in a dissipative scheme and a low-precision interpolation only near shock waves. This scheme is easily obtained by combining existing schemes often used in hypersonic flows. Its performance in a two-dimensional system is compared to existing schemes using two inviscid flows at Mach numbers 15 and 20. The results show that the scheme outperforms existing schemes in terms of improving accuracy around shock waves. It is also discovered that this scheme can prevent nonphysical numerical oscillations caused by a mismatch between grid and local-shock forms. The significance of the scheme is demonstrated in the interaction field between the normal shock wave and the boundary layer in competition between viscosity and numerical dissipations. Therefore, the current scheme is useful in a high-Mach-number problem.