Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
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
Multigrid
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 Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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
Recent developments in the multi-scale-finite-volume procedure
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Algebraic multiscale solver for flow in heterogeneous porous media
Journal of Computational Physics
Hi-index | 31.46 |
An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework. Motivated by the small pressure change inside highly conductive fractures, the fully coupled system is split into smaller systems, which are then sequentially solved. This splitting technique results in only one additional degree of freedom for each connected fracture network appearing in the matrix system. It can be interpreted as an agglomeration of highly connected cells; similar as in algebraic multigrid methods. For the solution of the resulting algebraic system, an i-MSFV method is introduced. In addition to the local basis and correction functions, which were previously developed in this framework, local fracture functions are introduced to accurately capture the fractures at the coarse scale. In this multiscale approach there exists one fracture function per network and local domain, and in the coarse scale problem there appears only one additional degree of freedom per connected fracture network. Numerical results are presented for validation and verification of this new iterative multiscale approach for fractured porous media, and to investigate its computational efficiency. Finally, it is demonstrated that the new method is an effective multiscale approach for simulations of realistic multiphase flows in fractured heterogeneous porous media.