A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
Convergence of a Nonconforming Multiscale Finite Element Method
SIAM Journal on Numerical Analysis
A mixed multiscale finite element method for elliptic problems with oscillating coefficients
Mathematics of Computation
Multiscale finite-volume method for compressible multiphase flow in porous media
Journal of Computational Physics
Journal of Computational Physics
Accurate multiscale finite element methods for two-phase flow simulations
Journal of Computational Physics
Iterative multiscale finite-volume method
Journal of Computational Physics
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
A Multilevel Multiscale Mimetic (M3) Method for an Anisotropic Infiltration Problem
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
A multiscale cell boundary element method for elliptic problems
Applied Numerical Mathematics
Journal of Computational Physics
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
Adaptive iterative multiscale finite volume method
Journal of Computational Physics
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Journal of Computational Physics
An iterative multiscale finite volume algorithm converging to the exact solution
Journal of Computational Physics
A stochastic mixed finite element heterogeneous multiscale method for flow in porous media
Journal of Computational Physics
A hierarchical fracture model for the iterative multiscale finite volume method
Journal of Computational Physics
A new multiscale computational method for elasto-plastic analysis of heterogeneous materials
Computational Mechanics
Recent developments in the multi-scale-finite-volume procedure
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
An adaptive multiscale method for density-driven instabilities
Journal of Computational Physics
Multi-scale stochastic simulation with a wavelet-based approach
Computers & Geosciences
Local-global multiscale model reduction for flows in high-contrast heterogeneous media
Journal of Computational Physics
Auxiliary variables for 3D multiscale simulations in heterogeneous porous media
Journal of Computational Physics
Hybrid Multiscale Finite Volume method for two-phase flow in porous media
Journal of Computational Physics
Block-spectral mapping for multi-scale solution
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
Application of a conservative, generalized multiscale finite element method to flow models
Journal of Computational and Applied Mathematics
Algebraic multiscale solver for flow in heterogeneous porous media
Journal of Computational Physics
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In this paper we present a multi-scale finite-volume (MSFV) method to solve elliptic problems with many spatial scales arising from flow in porous media. The method efficiently captures the effects of small scales on a coarse grid, is conservative, and treats tensor permeabilities correctly. The underlying idea is to construct transmissibilities that capture the local properties of the differential operator. This leads to a multi-point discretization scheme for the finite-volume solution algorithm. Transmissibilities for the MSFV have to be constructed only once as a preprocessing step and can be computed locally. Therefore this step is perfectly suited for massively parallel computers. Furthermore, a conservative fine-scale velocity field can be constructed from the coarse-scale pressure solution. Two sets of locally computed basis functions are employed. The first set of basis functions captures the small-scale heterogeneity of the underlying permeability field, and it is computed in order to construct the effective coarse-scale transmissibilities. A second set of basis functions is required to construct a conservative fine-scale velocity field. The accuracy and efficiency of our method is demonstrated by various numerical experiments.