A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
A mixed multiscale finite element method for elliptic problems with oscillating coefficients
Mathematics of Computation
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
Journal of Computational Physics
Iterative multiscale finite-volume method
Journal of Computational Physics
Modeling complex wells with the multi-scale finite-volume method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Adaptive iterative multiscale finite volume method
Journal of Computational Physics
An iterative multiscale finite volume algorithm converging to the exact solution
Journal of Computational Physics
An adaptive multiscale method for density-driven instabilities
Journal of Computational Physics
Hybrid Multiscale Finite Volume method for two-phase flow in porous media
Journal of Computational Physics
Generalized multiscale finite element methods (GMsFEM)
Journal of Computational Physics
Ensemble level multiscale finite element and preconditioner for channelized systems and applications
Journal of Computational and Applied Mathematics
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The Multiscale Finite-Volume (MSFV) method has been recently developed and tested for multiphase-flow problems with simplified physics (i.e. incompressible flow without gravity and capillary effects) and proved robust, accurate and efficient. However, applications to practical problems necessitate extensions that enable the method to deal with more complex processes. In this paper we present a modified version of the MSFV algorithm that provides a suitable and natural framework to include additional physics. The algorithm consists of four main steps: computation of the local basis functions, which are used to extract the coarse-scale effective transmissibilities; solution of the coarse-scale pressure equation; reconstruction of conservative fine-scale fluxes; and solution of the transport equations. Within this framework, we develop a MSFV method for compressible multiphase flow. The basic idea is to compute the basis functions as in the case of incompressible flow such that they remain independent of the pressure. The effects of compressibility are taken into account in the solution of the coarse-scale pressure equation and, if necessary, in the reconstruction of the fine-scale fluxes. We consider three models with an increasing level of complexity in the flux reconstruction and test them for highly compressible flows (tracer transport in gas flow, imbibition and drainage of partially saturated reservoirs, depletion of gas-water reservoirs, and flooding of oil-gas reservoirs). We demonstrate that the MSFV method provides accurate solutions for compressible multiphase flow problems. Whereas slightly compressible flows can be treated with a very simple model, a more sophisticate flux reconstruction is needed to obtain accurate fine-scale saturation fields in highly compressible flows.