The P(1-) RKDG Method for Two-Dimensional Euler Equations of Gas Dynamics

Abstract

Earlier work is continued on a class on nonlinearly stable Runge Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws. Two dimensional Euler equations for gas dynamics are solved using p1 elements. We discuss the generalization of the local projection, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions. Numerical examples include the standard regular shock reflection problem, the forward facing step problem and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of our approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods. Generalizations to pk elements with k equal to or greater than the use of adaptive triangulations to minimize local errors constitute ongoing research.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1991
Accession Number
ADA236842

Entities

People

  • Bernardo Cockburn
  • Chi-Wang Shu

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Computations
  • Decomposition
  • Dynamics
  • Equations
  • Euler Equations
  • Finite Element Analysis
  • Fluid Flow
  • Gas Dynamics
  • Geometry
  • Mathematics
  • Reflection
  • Standards
  • Triangles
  • Triangulation
  • Two Dimensional

Readers

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