Flux-Corrected Pseudospectral Method for Scalar Hyperbolic Conservation Laws

Abstract

The pseudospectral method has under-used advantages in problems involving shocks and discontinuities. These emerge from superior accuracy in phase and group velocities as compared to finite difference schemes of all orders. Dispersion curves for finite difference schemes suggest that group velocity error typically outranks Gibbs' error as a cause of numerical oscillation. A flux conservative form of the pseudospectral method is derived for compatibility with flux limiters used to preserve monotonicity. The resulting scheme gives high quality results in linear advection and shock formation/propagation examples. Keywords: Spectral techniques, Shock waves, Hyperbolic equations, Reprints, Inviscid flow.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1989
Accession Number
ADA226372

Entities

People

  • B. E. Mcdonald

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Advection
  • Amplitude
  • Chebyshev Polynomials
  • Discontinuities
  • Dispersion Relations
  • Dispersions
  • Equations
  • Errors
  • Fast Fourier Transforms
  • Fourier Series
  • Frequency
  • Group Velocity
  • Military Research
  • Oscillation
  • Phase Velocity
  • Square Waves

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)