Abstract
Abstract : The effort to use spectral methods to simulate flows with shock waves is summarized in four published papers. In (2) the authors study uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. Based on the new approximations, nonoscillatory spectral methods which possess the properties of both upwinding difference schemes and spectral methods were proposed. Numerical results are presented for the inviscid Burger's equation, and for one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock the problems, and the blast wave problem. Finally, the interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.
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