Monotone Multiscale Finite Volume Method for Flow in Heterogeneous Porous Media

Monotone Multiscale Finite Volume Method for Flow in Heterogeneous Porous Media

Wang, Y.
Hajibeygi, H.
Tchelepi, H.A.

Civil Engineering and Geosciences

Geoscience & Engineering

2014-09-08

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 is used for the 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.

http://resolver.tudelft.nl/uuid:889c0c65-e556-44c8-9496-efdaaad348f1

EAGE

ECMOR XIV: Proceedings 14th European Conference on Mathematics in Oil Recovery, Catania, Italy, 8-11 September 2014

Institutional Repository

conference paper

(c) 2014 The Author(s)