Space-marching gridless computation of steady supersonic/hypersonic flow

Abstract

Most computational fluid dynamics work uses Eulerian coordinates, which require generating a grid prior to flow field computation. Despite three decades of research, grid generation is still a bottleneck of CFD, as it is time-consuming, tedious and requires specialized training. It will be shown in this paper that using the unified coordinates introduced by Hui, there is no need for grid generation prior to flow computation; the grid is automatically generated while computing the flow. This greatly saves computing time. For steady super-sonic/hypersonic flow, the Euler equations of gas dynamics are of hyperbolic type and a space-marching gridless computation along the streamlines—coordinate lines in the unified coordinates—is shown to be a complete success in that: (a) it is most robust; (b) it resolves both slip lines (also called contact lines) and shocks sharply; (c) its computing time is more than three orders of magnitude smaller than Eulerian computation; and (d) it bypasses the tedious and time-consuming grid generation stage which is needed in Eulerian computation. Three examples are given to justify these claims.