Coordinate systems play a crucial role in the accurate computation of discontinuous flow. For two-dimensional steady supersonic flow the system based on streamlines and their orthogonals is found to be the optimal in that it is most robust and it produces infinite shock and slipline resolution. This system is also extended to two-dimensional unsteady (subsonic or supersonic) flow. However, such an optimal coor-dinate system is shown not to exist for general three-dimensional steady supersonic flow unless the flow velocity is perpendicular to the vorticity. Nevertheless, a system using stream surfaces as coordinate surfaces has the property of resolving slip surfaces crisply.
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