High Order Filtering Methods for Approximating Hyperbolic Systems of Conservation Laws

Abstract

In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed ENO (Essentially Non-Oscillatory) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. In this paper we develop a filtering method which uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, generally few in number, we use the full ENO apparatus, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. We obtain high order of accuracy in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method. Keywords: Charts; Burger equation; Contract discontinuity.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1990
Accession Number
ADA220930

Entities

People

  • F. Lafon
  • S. Osher

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Coefficients
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Discontinuities
  • Equations
  • Euler Equations
  • Filters
  • Filtration
  • Gas Dynamics
  • Iterations
  • Mathematical Filters
  • Numerical Analysis
  • Polynomials
  • Two Dimensional

Readers

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