TITLE:
A Method for the Solution of the 2D-Oswatitsch Equations
AUTHORS:
Volkmar Lorenz, Christian Mundt
KEYWORDS:
Oswatitsch, Mach Number Independence, Bow Shock, PDE, Time Dependent Solution, Ratios of Specific Heats
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.4,
April
29,
2016
ABSTRACT: Corresponding to Oswatitsch’s Mach number independence principle the Mach number of hypersonic inviscid flows, , does not affect components of various non-dimensional formulations such as velocity and density, pressure coefficients and Mach number behind a strong shock. On this account, the principle is significant in the development process for hypersonic vehicles. Oswatitsch deduced a system of partial differential equations which describes hypersonic flow. These equations are the basic gasdynamic equations as well as Crocco’s theorem which are reduced for the case of very high Mach numbers, . Their numerical solution can not only result in simplified algorithms prospectively utilized to describe the flow around bodies flying mainly in the lower stratosphere with very high Mach numbers. It also offers a deeper understanding of similarity effects for hypersonic flows. In this paper, a solution method for Oswatisch’s equations for perfect gas, based on a 4-step Runge-Kutta-algorithm, is presented including a fast shock-fitting procedure. An analysis of numerical stability is followed by a detailed comparison of results for different Mach numbers and ratios of the specific heats.