Accuracy and nonoscillatory properties of enslaved difference schemes

Donald Jones, Len G. Margolin, Andrew C. Poje

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We describe a general method for modifying a given finite-difference scheme by representing the effects of the subgrid scales in terms of the resolved scales through enslaving. The new scheme is more accurate in certain parameter regimes while retaining the time-step stability of the original scheme. We consider two general enslaving relations: an approximate enslaving based on truncation analysis and an exact enslaving based on the dynamics of the governing equation. We find that the modified schemes based on the exact enslaving eliminate unphysical oscillations, producing monotone solutions even when the original difference schemes do not, have this property. We offer a truncation analysis to justify this property. We apply our enslaving technique to advection-diffusion equations in both one and two spatial dimensions.

Original languageEnglish (US)
Pages (from-to)705-728
Number of pages24
JournalJournal of Computational Physics
Volume181
Issue number2
DOIs
StatePublished - Sep 20 2002

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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