Ws. Don et Cb. Quillen, NUMERICAL-SIMULATION OF SHOCK-CYLINDER INTERACTIONS .1. RESOLUTION, Journal of computational physics, 122(2), 1995, pp. 244-265
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.