TY - JOUR
T1 - Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS)
AU - Tene, Matei
AU - al Kobaisi, MS
AU - Hajibeygi, Hadi
PY - 2016
Y1 - 2016
N2 - This paper introduces an Algebraic MultiScale method for simulation of flow in heteroge-neous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and fracture networks. Then, amap between coarse-and fine-scale is obtained by algebraically computing basis functions with local support. In order to extend the localization assumption to the fractured media, four types of basis functions are investigated: (1)Decoupled-AMS, in which the two media are completely decoupled, (2)Frac-AMS and (3)Rock-AMS, which take into account only one-way transmissibilities, and (4)Coupled-AMS, in which the matrix and fracture interpolators are fully coupled. In order to ensure scalability, the F-AMS framework permits full flexibility in terms of the resolution of the fracture coarse grids. Numerical results are presented for two-and three-dimensional heterogeneous test cases. During these experiments, the performance of F-AMS, paired with ILU(0) as second-stage smoother in a convergent iterative procedure, is studied by monitoring CPU times and convergence rates. Finally, in order to investigate the scalability of the method, an extensive benchmark study is conducted, where a commercial algebraic multigrid solver is used as reference. The results show that, given an appropriate coarsening strategy, F-AMS is insensitive to severe fracture and matrix conductivity contrasts, as well as the length of the fracture networks. Its unique feature is that a fine-scale mass conservative flux field can be reconstructed after any iteration, providing efficient approximate solutions in time-dependent simulations.
AB - This paper introduces an Algebraic MultiScale method for simulation of flow in heteroge-neous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and fracture networks. Then, amap between coarse-and fine-scale is obtained by algebraically computing basis functions with local support. In order to extend the localization assumption to the fractured media, four types of basis functions are investigated: (1)Decoupled-AMS, in which the two media are completely decoupled, (2)Frac-AMS and (3)Rock-AMS, which take into account only one-way transmissibilities, and (4)Coupled-AMS, in which the matrix and fracture interpolators are fully coupled. In order to ensure scalability, the F-AMS framework permits full flexibility in terms of the resolution of the fracture coarse grids. Numerical results are presented for two-and three-dimensional heterogeneous test cases. During these experiments, the performance of F-AMS, paired with ILU(0) as second-stage smoother in a convergent iterative procedure, is studied by monitoring CPU times and convergence rates. Finally, in order to investigate the scalability of the method, an extensive benchmark study is conducted, where a commercial algebraic multigrid solver is used as reference. The results show that, given an appropriate coarsening strategy, F-AMS is insensitive to severe fracture and matrix conductivity contrasts, as well as the length of the fracture networks. Its unique feature is that a fine-scale mass conservative flux field can be reconstructed after any iteration, providing efficient approximate solutions in time-dependent simulations.
KW - Algebraic multiscale methods
KW - Flow in porous media
KW - Naturally fractured porous rock
KW - Heterogeneous permeability
KW - Scalable linear solvers
UR - http://resolver.tudelft.nl/uuid:c55b3ac8-ef38-4a34-ba54-2eaf44271b51
U2 - 10.1016/j.jcp.2016.06.012
DO - 10.1016/j.jcp.2016.06.012
M3 - Article
SN - 0021-9991
VL - 321
SP - 819
EP - 845
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -