Characteristic-mixed covolume methods for advection-dominated diffusion problems

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Characteristic-mixed covolume methods for time-dependent advection-dominated diffusion problems are developed and studied. The diffusion term in these problems is discretized using covolume methods applied to the mixed formulation of the problems on quadrilaterals, and the temporal differentiation and advection terms are treated by characteristic tracking schemes. Three characteristic tracking schemes are studied in the context of mixed covolume methods: the modified method of characteristics, the modified method of characteristics with adjusted advection, and the Eulerian-Lagrangian localized adjoint method. The proposed methods preserve the conceptual and computational merits of both characteristics-based schemes and the mixed covolume methods. Existence and uniqueness of a solution to the discrete problem arising from the methods is shown. Stability and convergence properties of these methods are also obtained; unconditionally stable results and error estimates of optimal order are established. Copyright (C) 2006 John Wiley & Sons, Ltd.
Publisher
JOHN WILEY & SONS LTD
Issue Date
2006-11
Language
English
Article Type
Article
Keywords

FINITE-ELEMENT METHODS; NAVIER-STOKES EQUATIONS; ELLIPTIC PROBLEMS; VOLUME METHODS; QUADRILATERAL GRIDS; FRAMEWORK

Citation

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, v.13, no.9, pp.677 - 697

ISSN
1070-5325
DOI
10.1002/nla.492
URI
http://hdl.handle.net/10203/20970
Appears in Collection
MA-Journal Papers(저널논문)
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