四个对激波与涡旋有高分辨率的计算格式的比较*

近十年来,计算非定常无粘可压气体力学Euler方程组的高分辨率差分格式有显着进展.本文选择四个近年受到重视的格式,用一较复杂的二维不定常问题作进一步的考验.所选算例为平面激波遇矩形障碍物初始阶段的绕射与反射.在挡板头部有两个尖角点,角点附近流场参量变化剧烈,会有中心稀疏波和集中涡的出现,要模拟好它们,就要求格式有较好的适应性.本文选择特殊的激波马赫数M_s=2.068,使静止坐标系下激波后流速恰为声速,并沿中心稀疏波区从角点发出的一条曲线也有这一现象,以考察各格式在方程组某一特征值恰为零时的计算特点,因零特征值可以使某些格式局部受损.计算结果的图形显示可表明四个格式在激波分辨率,格式粘性、膨胀波的计算、模拟非定常集中涡产生过程的能力等方面的性质.

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

In recent ten years high rosolution difference schemes for the computation of the full unsteady Eulerian system of equations for invisid compressible gas finds celebrated progress.This paper tests,by a complex two-dimensional unsteady problem,four recent schemes.to them further attention is 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 the top side there are two sharp corners, near which flow parameters finds severe variation. There is an 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 M_s=2.068 is so chosen,that at this M_s the partial velocity behind impinging shock in fixed coordinate system is right cqual to the speed of sound there,this condition also oceurs along a curve in the region of expansion fan with a center at the corner. This can clarify the computational feature of dif-ferent 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.