Print Email Facebook Twitter Monotone multiscale finite volume method Title Monotone multiscale finite volume method Author Wang, Y. Hajibeygi, H. Tchelepi, H.A. Faculty Civil Engineering and Geosciences Department Geoscience & Engineering Date 2015-08-16 Abstract The MultiScale Finite Volume (MSFV) method is known to produce non-monotone solutions. The causes of the non-monotone solutions are identified and connected to the local flux across the boundaries of primal coarse cells induced by the basis functions. We propose a monotone MSFV (m-MSFV) method based on a local stencil-fix that guarantees monotonicity of the coarse-scale operator, and thus, the resulting approximate fine-scale solution. Detection of non-physical transmissibility coefficients that lead to non-monotone solutions is achieved using local information only and is performed algebraically. For these ‘critical’ primal coarse-grid interfaces, a monotone local flux approximation, specifically, a Two-Point Flux Approximation (TPFA), is employed. Alternatively, a local linear boundary condition can be used for the dual basis functions to reduce the degree of non-monotonicity. The local nature of the two strategies allows for ensuring monotonicity in local sub-regions, where the non-physical transmissibility occurs. For practical applications, an adaptive approach based on normalized positive off-diagonal coarse-scale transmissibility coefficients is developed. Based on the histogram of these normalized coefficients, one can remove the large peaks by applying the proposed modifications only for a small fraction of the primal coarse grids. Though the m-MSFV approach can guarantee monotonicity of the solutions to any desired level, numerical results illustrate that employing the m-MSFV modifications only for a small fraction of the domain can significantly reduce the non-monotonicity of the conservative MSFV solutions. Subject multiscale finite volume methoditerative multiscale methodsalgebraic multiscale solverscalable linear solversmonotone flux approximation schemesmultipoint flux approximationporous media To reference this document use: http://resolver.tudelft.nl/uuid:16511dd6-dbb6-4c1e-b502-f770d860aa09 Publisher Springer ISSN 1420-0597 Source https://doi.org/10.1007/s10596-015-9506-7 Source Computational Geosciences, 2015 Part of collection Institutional Repository Document type journal article Rights (c) 2015 The Author(s)This article is published with open access at Springerlink.com Files PDF Hajibeygi_2015.pdf 12.18 MB Close viewer /islandora/object/uuid:16511dd6-dbb6-4c1e-b502-f770d860aa09/datastream/OBJ/view