C Xxxx Society for Industrial and Applied Mathematics Self-similar Solutions for the Triple Point Paradox in Gasdynamics *-猫眼课题宝

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A. Tesdall;R. Sanders;B. Keyfitz

本文给出了描述弱激波马赫反射的可压缩欧拉方程的二维Riemann问题的数值解。采用高分辨率有限体积格式求解自相似变量的方程。我们使用极端的局部网格细化解决方案的一个明显的，但数学上不允许的冲击三相点附近。这些解包含一个复杂的结构：不是三个激波在一个标准的三相点中相遇，而是一个三相点序列和领先三相点后面的微小超音速斑块，由音速线和马赫激波之间的弱激波和膨胀波的反射形成。一个膨胀扇起源于每个三相点，解决了冯诺依曼三相点悖论。1.导论.考虑一个无粘、可压缩、理想气体中的平面正激波，如图1所示，它撞击一个具有半角θ w的固定楔形体。对于密度ρ = ρ r，速度u =（u，v）=（0，0）和压力p = pr的给定上游状态，快速（即，u + c）冲击由下式给出：

We present numerical solutions of a two-dimensional Riemann problem for the com-pressible Euler equations that describes the Mach reflection of weak shock waves. High resolution finite volume schemes are used to solve the equations formulated in self-similar variables. We use extreme local grid refinement to resolve the solution in the neighborhood of an apparent but mathematically inadmissible shock triple point. The solutions contain a complex structure: instead of three shocks meeting in a single standard triple point, there is a sequence of triple points and tiny supersonic patches behind the leading triple point, formed by the reflection of weak shocks and expansion waves between the sonic line and the Mach shock. An expansion fan originates at each triple point, resolving the von Neumann triple point paradox. 1. Introduction. Consider a plane normal shock in an inviscid, compressible, perfect gas which hits a fixed wedge with half angle θ w , as depicted in Figure 1. For a given upstream state with density ρ = ρ r , velocity u = (u, v) = (0, 0), and pressure p = p r , the fluid properties downstream of a fast (i.e., u + c) shock are given by

C Xxxx Society for Industrial and Applied Mathematics Self-similar Solutions for the Triple Point Paradox in Gasdynamics *

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