无粘流中能捕捉较弱的接触间断和激波的反扩散差分格式

A DIFFERENCE SCHEME WITH ANTI DIFFUSION TERMS WHICH CAN CAPTURE WEAK CONTACT DISCONTINUI TIES AND SHOCKS IN INVISCID FLOW

在研究弱入射激波遇到对称楔以后的马赫反射现象时，激波管实验不易测出很弱的接触间断，也不易捕捉到马赫反射与正规反射转换的条件。文章一方面研究了可压流体力学欧拉方程的数值方法，首先是用反扩散法改进接触间断的计算；另一方面根据格式粘性的特性和它引出的很微小的熵的变化规律来显示很弱的接触间断和反射激波。这样才易于将对三波点的分析推进一步。文［５，６］曾预言了一种反散波是连续的压缩波的新的激波反射类型。我们设想并根据计算初步确认这新类型反射实际应该是简单马赫反射，反射波虽弱仍是激波。

It is not easy for shock tube experiments to detect very weak contact discontinuities when studying the Mach reflection occurred after a weak shock colliding on a symmetric wedge, also difficult to catch the transition condition between Mach reflection and regular reflection. For this purpose a numerical method for solving Euler's equations in compressible flow is presented, the key is to improve the computation of contact discontinuities using anti diffusion method; equally important is to identify the very weak contact discontinuity and the reflected wave by taking advantage of the behavior of the scheme viscosity and the resulted very small entropy peak. Only doing like this, the analysis of the triple point can be advanced.In,a new type of reflection in irregular reflection with a compression wave without jump was predicated and called “von Neumann wave”. We judge and confirm by computational results that the “new” type of reflection must be a simple Mach reflection. Even though very weak, the reflected wave in irregular reflection is still a shock. A systematic calculation about the transition condition will be presented in another paper.