A Minimum Entropy Principle of High Order Schemes for Gas Dynamics Equations

Abstract

The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy [10]. First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes [6] also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations in [13, 14], to enforce the minimum entropy principle for high order finite volume and discontinuous Galerkin (DG) schemes.

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Document Details

Document Type
Technical Report
Publication Date
Jul 18, 2011
Accession Number
ADA557667

Entities

People

  • Chi-Wang Shu
  • Xiangxiong Zhang

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Convex Sets
  • Dynamics
  • Equations
  • Errors
  • Euler Equations
  • Gas Dynamics
  • Mathematics
  • Physics
  • Polynomials
  • Runge Kutta Method
  • Shock Tubes
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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