An efficient parallel mixed method for flow simulations in heterogeneous geological media. (English) Zbl 1372.86009
Summary: The permeability of a 3D geological fracture network is determined by triangulating the fractures and solving the 2D Darcy’s equation in each fracture. Here, the numerical modelling aims to simulate a great number of networks made up of a great number of fractures i.e. from \(10^{3}\) to \(10^{6}\) fractures. Parallel computing allows us to solve very large linear systems improving the realism of simulations. Several algorithms to simulating fluid flow are proposed for the cases of significant matrix permeability. In the case of a weak permeability matrix, the flow is focused in the fractures having a strong permeability and fluids percolate through networks of interconnected fractures. In this paper, we present a complete parallel algorithm for solving flow equations in fracture networks. We consider an imprevious matrix. The different parts of the algorithm are detailed. Numerical examples using the mixed finite element (MFE) method for various fracture networks illustrate the efficiency and robustness of the proposed algorithm. To the best of our knowledge, results for parellel simulation of fluid flow in discrete-fractured media with impervious matrix using the MFE method are the first to appear in the literature.
MSC:
| 86A60 | Geological problems |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
parallel computing; geological media; fluid flow; triangular mesh; mixed finite element methodSoftware:
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