Section: New Results

Models and simulations for flow in fractured media

This work is done in collaboration with J.-R. de Dreuzy, from the department of Geosciences at the University of Rennes 1 (who is on leave until 2013 at UPC, Barcelona, Spain). It is done in the context of the Micas project ( 8.1.2 ).

A Ph-D thesis was defended this year [13] .

Domain decomposition method for flow in 3D networks of fractures

Participants : Jocelyne Erhel, Baptiste Poirriez.

This work was presented at a conference and published in the proceedings of another conference [29] , [32] . A paper is in preparation.

This paper aims at solving efficiently the linear system arising from flow computations in Discrete Fracture Networks (DFN). We define a partition of fractures into connected sets and apply a Schur domain decomposition method. Conjugate Gradient is preconditioned by Neumann-Neumann and deflation. Preliminary results with one network show the ability of our method to reduce both the number of iterations and the computational time.

Mortar method for flow in 3D networks of fractures

Participants : Jocelyne Erhel, Géraldine Pichot.

This work is published in a journal [20] .

The simulation of flow in fractured media requires handling both a large number of fractures and a complex interconnecting network of these fractures. Networks considered in this paper are 3D domains made up of 2D fractures intersecting each other and randomly generated. Due to the stochastic generation of fractures, intersections can be highly intricate. The numerical method must generate a mesh and define a discrete problem for any Discrete Fracture Network (DFN). A first approach [51] is to generate a conforming mesh and to apply a mixed hybrid finite element method. However the resulting linear system becomes very large when the network contains many fractures. Hence a second approach [52] is to generate a non conforming mesh, using an independent mesh generation for each fracture. Then a Mortar technique applied to the mixed hybrid finite element method deals with the non-matching grids. When intersections do not cross nor overlap, pairwise Mortar relations for each intersection are efficient [52] . But for most of random networks, discretized intersections involve more than two fractures. In this paper, we design a new method generalizing the previous one and applicable for stochastic networks. The main idea is to combine pairwise Mortar relations with additional relations for the overlapping part. This method still ensures the continuity of fluxes and heads and still yields a symmetric positive definite linear system. Numerical experiments show the efficiency of the method applied to complex stochastic fracture networks. We also study numerical convergence when reducing the mesh step. This method makes it easy to perform mesh optimization and appears as a very promising tool to simulate flow in multiscale fracture networks.