Characteristic-mixed covolume methods for advection-dominated diffusion problems

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 a...

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Bibliographic Details
Published in:Numerical linear algebra with applications 2006-11, Vol.13 (9), p.677-697
Main Authors: Chen, Zhangxin, Chou, So-Hsiang, Kwak, Do Young
Format: Article
Language:English
Subjects:
advection-dominated diffusion problem
characteristics-based method
control volume finite element method
control volume method
convergence
covolume method
error estimate
finite element method
finite volume method
mixed finite element method
stability
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Summary: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 © 2006 John Wiley & Sons, Ltd.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.492