Numerical Methods for Systems of Conservation Laws of Mixed Type Using Flux Splitting

Abstract

Numerical methods for solving systems of conservation laws of mixed hyperbolic-elliptic type are investigated, through a flux splitting to write the physical elliptic flux as a sum of two hyperbolic fluxes with positive/negative eigenvalues, then to apply the essentially non-oscillatory (ENO) high order finite difference methods on each of them. The method, in the simplest first order case, is equivalent to adding a numerical dissipation term with a diagonal dissipation matrix. The numerical results on the van der Waals equation of gas dynamics indicate that the method can resolve phase boundaries well and can be used as a tool to study the evolution of elliptic regions. More numerical tests on different mixed type equations constitute current research. (kr)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1990
Accession Number
ADA227108

Entities

People

  • Chi-Wang Shu

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Computers
  • Differential Equations
  • Dissipation
  • Eigenvalues
  • Engineering
  • Equations
  • Error Analysis
  • Euler Equations
  • Fluid Dynamics
  • Gas Dynamics
  • Numerical Analysis
  • Phase Transformations

Fields of Study

  • Mathematics

Readers

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