A Comparison of Four Recent Numerical Schemes Giving High Resolution of Shock Wave and Concentrated Vortex

In recent ten years high resolution difference schenies for the computation of thefull unsteady Eulerian system of equations for invisid compressible gas finds celebratedprogress.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 stageof a two-dimensional diffraction and reflection of a plane shock wave,impinging on arectangular 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 centerand also concentrated vortices.To simulate them well,the schemes should have goodadaptivity.The special shock Mach number M_s=2.068 is so chosen,that at this M_s,the partical velocity behind impinging shock in fixed coordinate system is just equal tothe speed of sound there,this condition also occurs along a curve in the region ofexpansion fan with a center at the corner.This can clarify the computational featureof different schemes in case,when one of the eigenvalues is just zero.Zero eigenvaluemay spoil some schemes locally.Graphical visualization of the computational resultsmay,show features of the tested schemes about the shock wave resolution,schemeviscosity,expansion wave and the ability.to simulate the process of the generation ofunsteadv concentrated vortex.