A comparison of four recent numerical schemes giving high resolution of shock wave and concentrated vortex

Abstract

In recent ten years high resolution difference schemes for the computation of the full unsteady Eulerian system of equations for invisid compressible gas finds celebrated progress. This paper tests furtherly, by a complex two-dimensional unsteady problem, four recent schemes, to them attentions are paid. The test problem is the initial stage of a two-dimensional diffraction and reflection of a plane shock wave, impinging on a rectangular obstacle. At whose top side there are two sharp corners, near which flow parameters finds severe variation. There is occurrence of expansion fan with a center and also concentrated vortices. To simulate them well, the schemes should have good adaptivity. The special shock Mach number M1=2.068 is so chosen, that at this M1 the partical velocity behind impinging shock in fixed coordinate system is just equal to the speed of sound there, this condition also occurs along a curve in the region of expansion fan with a center at the corner. This can clarify the computational feature of different schemes in case, when one of the eigenvalues is just zero. Zero eigenvalue may spoil some schemes locally. Graphical visualization of the computational results may show features of the tested schemes about the shock wave resolution, scheme viscosity, expansion wave and the ability to simulate the process of the generation of unsteady concentrated vortex.