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An Analysis of Smoothing Effects of Upwinding Strategies for the Convection-Diffusion Equation
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An Analysis of Smoothing Effects of Upwinding Strategies for the Convection-Diffusion Equation
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Journal Article
An Analysis of Smoothing Effects of Upwinding Strategies for the Convection-Diffusion Equation
2003
Overview
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.
Publisher
Society for Industrial and Applied Mathematics
Subject
/ Convection diffusion equation
/ Difference and functional equations, recurrence relations
/ Exact sciences and technology
/ Matrices
/ Numerical analysis. Scientific computation
/ Partial differential equations
/ Partial differential equations, boundary value problems
/ Sciences and techniques of general use
/ Stencils
