Abstract: 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.

Key words: weak discontinuity, weak Mach reflection, anti-diffusion, difference scheme, inviscid flow