Positivity-preserving High Order Finite Difference WENO Schemes for Compressible Euler Equations

Abstract

In [20, 21, 23], we constructed uniformly high order accurate discontinuous Galerkin (DG) and finite volume schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. In this paper, we present an extension of this framework to construct positivity-preserving high order essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) finite difference schemes for compressible Euler equations. General equations of state and source terms are also discussed. Numerical tests of the fifth order finite difference WENO scheme are reported to demonstrate the good behavior of such schemes.

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Document Details

Document Type
Technical Report
Publication Date
Jul 15, 2011
Accession Number
ADA557715

Entities

People

  • Chi-Wang Shu
  • Xiangxiong Zhang

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Chemical Reactions
  • Computational Fluid Dynamics
  • Computational Science
  • Dynamics
  • Eigenvalues
  • Equations
  • Equations Of State
  • Euler Equations
  • Fluid Dynamics
  • Gas Dynamics
  • Low Density
  • Mathematics
  • Physics
  • Polynomials
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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