The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V: Multidimensional Systems,

Abstract

This is the fifth paper in a series in which we construct and study the so-called Range-Kutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are described and discussed, including algorithm formulation and practical implementation issues such as the numerical fluxes, quadrature rules, degrees of freedom, and the slope limiters, both in the triangular and the rectangular element cases. Numerical experiments for two dimensional Euler equations of compressible gas dynamics are presented that show the effect of the (formal) order of accuracy and the use of triangles or rectangles, on the quality of the approximation.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1997
Accession Number
ADA329450

Entities

People

  • Bernardo Cockburn
  • Chi-Wang Shu

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Gas Dynamics
  • Geometry
  • Mathematics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Polynomials
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)