A Second Order Upwind Flux Method for Hyperbolic Conservation Laws.

Abstract

We present first- and second-order upwind schemes employing a numerically calculated characteristic speed direction and combine them into a simple monotonicity preserving hybrid scheme using the method of flux correction. The first-order scheme is constructed to maintain accuracy at flow reversal points. The hybrid scheme computes a provisional update from the first-order scheme, and then filters the second-order corrections to prevent occurrence of new extrema. We derive analytic solutions for a developing N-wave shock, and compare computed versus analytic results for two different N waves and for a third case involving linear advection of a square wave. Results are given with and without the second-order correction. The second-order results are always superior to first-order results, with the most dramatic difference occurring for the case of linear advection. The results suggest that higher order differences could be substituted in the hybrid scheme to reduce truncation error even further.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1983
Accession Number
ADA139769

Entities

People

  • B. E. Mcdonald

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Acoustics
  • Advection
  • Algorithms
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Errors
  • Fluid Dynamics
  • Military Research
  • Navy
  • Partial Differential Equations
  • Research Facilities
  • Square Waves
  • Waves

Fields of Study

  • Mathematics

Readers

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