Method of Characteristics with Simplicial Nets

The approximation of stationary compressible flows by means of a time-dependent technique has been considered in the past by many authors /1/–/4/. Especially in the blunt-body supersonic flow problem this procedure is widely used leading to results which can be compared with experimental data /5/ or with other analytical approaches which are asymptotically valid in the transonic flow region /6/. Normally the limit solution of a simulated time-dependent flow is reached on the computer after a very large number of iterations. Therefore the question arises how much the solution is influenced by the errors which are introduced into the calculation by the artificial time dependence. A reliable answer can be given if one knows the exact solution of the stationary flow field. Then the absolute error is known and its amplification can be computed from one time step to the other. For the RINGLEB-flow /7/ the exact values of all the flow field quantities are known. This special type of flow which includes subsonic, transonic and supersonic regions can be used as a standard for comparison of time-dependent techniques with respect to error growth.