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The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

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

Elman, H.C. and Ramage, A. (2002) An analysis of smoothing effects of upwinding strategies for the convection-diffusion equation. SIAM Journal on Numerical Analysis, 40 (1). pp. 254-281. ISSN 0036-1429

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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.