Title: Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS),
Abstract: This paper introduces an Algebraic MultiScale method for simulation of flow
in heterogeneous porous media with embedded discrete Fractures (F-AMS). First,
multiscale coarse grids are independently constructed for both porous matrix
and fracture networks. Then, a map 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.