An analysis of smoothing effects of upwinding strategies for the convection-diffusion equation

H.C. Elman, A. Ramage

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Using a technique for constructing analytic expressions for discrete solutions to the convection-diffusion equation, we examine and characterize the effects of upwinding strategies on solution quality. In particular, for grid-aligned flow and discretization based on bilinear finite elements with streamline upwinding, we show precisely how the amount of upwinding included in the discrete operator affects solution oscillations and accuracy when different types of boundary layers are present. This analysis provides a basis for choosing a streamline upwinding parameter which also gives accurate solutions for problems with non-grid-aligned and variable speed flows. In addition, we show that the same analytic techniques provide insight into other discretizations, such as a finite difference method that incorporates streamline diffusion and the isotropic artificial diffusion method.
Original languageEnglish
Pages (from-to)254-281
Number of pages27
JournalSIAM Journal on Numerical Analysis
Volume40
Issue number1
DOIs
Publication statusPublished - 2002

Keywords

  • convection-diffusion equation
  • oscillations
  • Galerkin finite element method
  • streamline diffusion

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