Supersonic Flow over Bodies of Revolution (With Special Reference to High Speed Computing)

摘要

With the advent of large-scale high-speed computing machines, it has become feasible to solve certain supersonic flow problems by numerical methods using the exact hydrodynamical equations instead of resorting to linearization or graphical methods. This report describes in detail one such numerical method; namely, an efficient form of the method of characteristics. Characteristic equations are derived for supersonic, steady, inviscid, isoenergetic flows in terms of a variety of dependent variables. A discussion is given of several methods of numerically solving systems of 1st order ordinary differential equations, such as are encountered in the Taylor-Maccoll and corner processes. The other computations involve approximating partial derivatives by difference quotients and solving on a finite grid of points. Solutions are derived for the cases in which the derivatives are approximated to 1st, 2nd, and 3rd orders. An empirical study is made of the error due to the introduction of finite differences. This is based on the results of a particular calculation performed on the ENIAC. It is shown that a knowledge of the nature of the errors leads to a procedure for extrapolation to zero grid size, which reduces by a factor of ten the total labor required to obtain a solution correct to about four significant figures. (Author)