An iterative Multiscale Finite-Volume algorithm converging to the exact solution

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Serval ID
serval:BIB_3A25E1060FD9
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
An iterative Multiscale Finite-Volume algorithm converging to the exact solution
Journal
Journal of Computational Physics
Author(s)
Lunati I., Tyagi M., Lee S.H.
Publication state
Published
Issued date
2011
Peer-reviewed
Oui
Volume
230
Number
5
Pages
1849-1864
Language
english
Abstract
The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).
Create date
20/04/2012 9:16
Last modification date
20/08/2019 13:29
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