NUMERICAL-SIMULATION OF SHOCK-CYLINDER INTERACTIONS .1. RESOLUTION

We apply two different high-order shock capturing schemes to the study of a two-dimensional unsteady inviscid flow. In particular, we study the interaction of a planar shock with a cylindrical volume of a light gas (helium or hydrogen) contained in air. The two schemes used are t he Chebyshev collocation method and the ENO finite difference scheme o f Osher and Shu, and they are applied to a physical model consisting o f the Euler equations with a real gas equation of state and multiple c hemical species. The parallel implementation and low-level coding of t he ENO scheme on the Thinking Machines CM-5 results in much higher per formance than is possible on a standard serial or vector machine. The ENO code is compared with an existing experimental result and agrees w ell with it. The results of spectral and ENO calculations are then com pared with each other at different resolutions for a Mach 2 interactio n. The spectral scheme, though highly oscillatory in nature for discon tinuous problems (Gibbs), accurately predicts both large and fine scal e structures of the interaction between the shock and the light gas cy linder. Good results can be recovered from the spectral results by pos t-processing the raw numerical data to remove the Gibbs phenomena. The se results are compared with the ENO schemes. The comparison is progre ssively better as the grid refinement and numerical order of the ENO s cheme is increased. This demonstrates definitively the applicability a nd value of high order schemes to flows with shocks and complicated no n-linear physics. (C) 1995 Academic Press, Inc.