An operator formulation of the multiscale finite-volume method with correction function

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Publications
Institution
Title
An operator formulation of the multiscale finite-volume method with correction function
Journal
Multiscale Modeling and Simulation
Author(s)
Lunati I., Lee S.H.
ISSN
1540-3459
Publication state
Published
Issued date
2009
Peer-reviewed
Oui
Volume
8
Number
1
Pages
96-109
Language
english
Abstract
The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.
Keywords
multiscale finite-volume method, domain decomposition, single-cell overlap, multiscale methods, multiphase flow in porous media, reservoir simulations
Open Access
Yes
Create date
20/02/2010 11:53
Last modification date
20/08/2019 15:47
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