Large Time Step Shock-Capturing Techniques for Scalar Conservation Laws,

Abstract

For a scalar conservation law u sub t = f(u) sub x with f'' of constant sign, the first order upwind difference scheme is a special case of Godunov's method. The method is equivalent to solving a sequence of Riemann problems at each step and averaging the resulting solution over each cell in order to obtain the numerical solution at the next time level. The difference scheme is stable (and the solutions to the associated sequence of Riemann problems do not interact) provided the Courant number nu is less than 1. By allowing and explicitly handling such interactions, it is possible to obtain a generalized method which is stable for nu much larger than 1. In many cases the resulting solution is considerably more accurate than solutions obtained by other numerical methods. In particular, shocks can be correctly computed with virtually no smearing. The generalized method is rather unorthodox and still has some problems associated with it. Nonetheless, preliminary results are quite encouraging. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1981
Accession Number
ADA109847

Entities

People

  • Randall J. LeVeque

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Cauchy Problem
  • Coefficients
  • Computer Science
  • Differential Equations
  • Discontinuities
  • Equations
  • Interpolation
  • Linear Accelerators
  • Method Of Characteristics
  • Numerical Analysis
  • Partial Differential Equations
  • Rarefaction
  • Sequences
  • Shock
  • Step Functions
  • Waves

Fields of Study

  • Mathematics

Readers

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