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Determination of Optimal Upstream Weighting Parameter for the Finite Element Solution of Transient Transport Equation
Author(s) -
Honma S.,
Karadi G.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860661010
Subject(s) - weighting , transient (computer programming) , method of mean weighted residuals , upstream (networking) , finite element method , residual , dispersion (optics) , convection–diffusion equation , péclet number , mathematics , galerkin method , numerical analysis , mechanics , flow (mathematics) , mathematical analysis , physics , algorithm , computer science , optics , thermodynamics , acoustics , computer network , operating system
In this study the results of a numerical experiment involving the finite element solution of the convection‐dominated transport equation are presented. It is shown that, for large Peclet numbers, the standard Galerkin approach produces unacceptable oscillations. Although the upstream weighting residual method eliminates this problem for steady state problems, its application to transient flow problems has received considerable criticism, because false dispersion and/or the smearing of steep gradients are observed. The numerical experiments performed for transient problems revealed that the upstream weighting residual method can be improved considerably if the upstream weighting parameter is selected as a function of the Courant number. Based on the results of these numerical experiments, a relationship between the optimal weighting parameter and the Courant number is proposed so that oscillations are eliminated and false dispersion is reduced to an acceptable level.