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Characteristic‐mixed covolume methods for advection‐dominated diffusion problems
Author(s) -
Chen Zhangxin,
Chou SoHsiang,
Kwak Do Young
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.492
Subject(s) - mathematics , discretization , advection , context (archaeology) , convergence (economics) , stability (learning theory) , uniqueness , diffusion , term (time) , mathematical optimization , mathematical analysis , computer science , thermodynamics , geology , paleontology , physics , quantum mechanics , machine learning , economic growth , economics
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.