The Stream-Function Coordinate System for Solution of Unsteady-Compressible-Flow Problems

摘要

A computer program which solves two dimensional parabolic flow problems was adapted to solve one dimensional compressible flow problems which involve solution of hyperbolic equations. The governing differential equations are formulated in a stream function coordinate system. Implicit finite difference equivalents of these equations are solved by use of this computer program. The advantages of using a floating grid system are demonstrated by solving two problems: (1) the sudden stopping of steady flow, and (2) the shock tube. The physical realism and numerical accuracy of predictions are also discussed. It is observed that this method predicts a flow field which matches the exact solution fairly well. A notable feature of this procedure is its ability to locate the discontinuities in the temperature and density profiles.