UNIFORM HIGH-ORDER SPECTRAL METHODS FOR ONE-DIMENSIONAL AND 2-DIMENSIONAL EULER EQUATIONS

In this paper we study uniform high-order spectral methods to solve multi-dimensional Euler gas dynamics equations. Uniform high-order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the essentially non-oscillatory polynomial (ENO) interpolations into the spectral methods. Based on the new approximations, we propose nonoscillatory spectral methods which possess the properties of both upwinding difference schemes and spectral methods. We present numerical results for inviscid Burgers' equation, various one-dimensional Euler equations including the interactions between a shock wave and density disturbances, Sod's and Lax's, and blast wave problems. Finally, we simulate the interaction between a March-3 two-dimensional shock wave and a rotating vortex. © 1993 Academic Press. All rights reserved.