Most CFD work use Eulerian coordinates,which re- quire generating a grid prior to flow filed 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 et.al.[1–4],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 by-passes the tedious and time- consuming grid generation stage which is needed in Eulerian computation.Three examples are given to justify these claims.
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