Uniform High Order Spectral Methods for One and Two Dimensional Euler Equations
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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This paper studies 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 approximation, we propose nonoscillatory spectral methods which possess the properties of both upwinding difference scheme and spectral methods. We present numerical results for the inviscid Burgers equation, and for one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sods and Laxs shock tube problems, and the blast wave problem. Finally, we simulate the interaction between a Mach 3 two dimensional shock wave and a rotating vortex.
- Fluid Mechanics