Compact mixed methods for convection/diffusion type problems

This paper presents a class of fourth-order compact finite difference technique for solving two-dimensional convection diffusion equation. The equation is recasted as a first-order mixed system, introducing a conservation and flux equations. Since flux appears explicitly in the mixed formulation, we...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 218; no. 10; pp. 5867 - 5876
Main Authors Abide, Stéphane, Chesneau, Xavier, Zeghmati, Belkacem
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2012
Subjects
Approximation
Compact difference schemes
Convection
Convection/diffusion equation
Convergence
Diffusion
Finite difference method
Flux
High accuracy
Mathematical analysis
Mathematical models
Compact difference schemes
High accuracy
Convection/diffusion equation
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Summary:This paper presents a class of fourth-order compact finite difference technique for solving two-dimensional convection diffusion equation. The equation is recasted as a first-order mixed system, introducing a conservation and flux equations. Since flux appears explicitly in the mixed formulation, we search a fourth-order compact approximation of the primary solution field and flux. Based on Taylor series expansion, the proposed compact mixed formulation generalizes the work of Carey and Spotz [G.F. Carey, W.F. Spotz, Higher-order compact mixed methods, Commun. Numer. Meth. Eng. 13 (1997)]. We show that their fourth-order formulation corresponds to a particular case of our presented scheme, and we extend their work to variable diffusion and convection coefficients. Some numerical experiments are performed to demonstrate the fourth-order effective convergence rate.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.11.027