Uniform High Order Spectral Methods for One and Two Dimensional Euler Equations

Abstract

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, Sod's and Lax's 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.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1991
Accession Number
ADA234180

Entities

People

  • Chi-Wang Shu
  • Wei Cai

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Blast Waves
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Discontinuities
  • Equations
  • Euler Equations
  • Flow
  • Fluid Flow
  • Gas Dynamics
  • Mathematics
  • Polynomials
  • Turbulent Flow
  • Two Dimensional
  • Waves

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)