Numerical Simulation of Shock-Cylinder Interactions: Ⅰ. Resolution

摘要

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 the Chebyshev collocation method and the ENO finite difference scheme of Osher and Shu, and they are applied to a physical model consisting of the Euler equations with a real gas equation of state and multiple chemical species. The parallel implementation and low-level coding of the ENO scheme on the Thinking Machines CM-5 results in much higher performance than is possible on a standard serial or vector machine. The ENO code is compared with an existing experimental result and agrees well with it. The results of spectral and ENO calculations are then compared with each other at different resolutions for a Mach 2 interaction. The spectral scheme, though highly oscillatory in nature for discontinuous problems (Gibbs), accurately predicts both large and fine scale structures of the interaction between the shock and the light gas cylinder. Good results can be recovered from the spectral results by post-processing the raw numerical data to remove the Gibbs phenomena. These results are compared with the ENO schemes. The comparison is progressively better as the grid refinement and numerical order of the ENO scheme is increased. This demonstrates definitively the applicability and value of high order schemes to flows with shocks and complicated non-linear physics.