Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
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
Homogenization via p-FEM for problems with microstructure
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
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
A stochastic variational multiscale method for diffusion in heterogeneous random media
Journal of Computational Physics
Multiscale finite element methods for porous media flows and their applications
Applied Numerical Mathematics
A multilevel multiscale mimetic (M3) method for two-phase flows in porous media
Journal of Computational Physics
Iterative multiscale finite-volume method
Journal of Computational Physics
A stochastic multiscale framework for modeling flow through random heterogeneous porous media
Journal of Computational Physics
Journal of Computational Physics
Applied Numerical Mathematics
Multiscale finite element methods for high-contrast problems using local spectral basis functions
Journal of Computational Physics
Enhanced linearized reduced-order models for subsurface flow simulation
Journal of Computational Physics
A new multiscale computational method for elasto-plastic analysis of heterogeneous materials
Computational Mechanics
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
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
Mode decomposition methods for flows in high-contrast porous media. A global approach
Journal of Computational Physics
Application of a conservative, generalized multiscale finite element method to flow models
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 31.51 |
In this paper we propose a modified multiscale finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the global fine-scale solution at initial time to determine the boundary conditions of the basis functions. This method provides a significant improvement in two-phase flow simulations in porous media where the long-range effects are important. This is typical for some recent benchmark tests, such as the SPE comparative solution project [M. Christie, M. Blunt, Tenth spe comparative solution project: a comparison of upscaling techniques, SPE Reser. Eval. Eng. 4 (2001) 308-317], where porous media have a channelized structure. The use of global information allows us to capture the long-range effects more accurately compared to the multiscale finite element methods that use only local information to construct the basis functions. We present some analysis of the proposed method to illustrate that the method can indeed capture the long-range effect in channelized media.