Triangle Based TVD (Total Variation Diminishing) Schemes for Hyperbolic Conversation Laws

Abstract

A triangle based TVD (total variation diminishing) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedure. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux to second order accuracy. Numerical results for linear advection and Burgers' equation are presented. Keywords: Hyperbolic conservation laws; Limiters; Triangular threads.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA218144

Entities

People

  • Bjorn Engquist
  • Louis J. Durlofsky
  • Stanley Osher

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Aeronautics
  • Boundaries
  • Computers
  • Consortiums
  • Convergence
  • Engineering
  • Equations
  • Errors
  • Finite Element Analysis
  • Geometry
  • Grids
  • Integrals
  • Interpolation
  • Mathematics
  • Triangles
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space