Study and implementation of a domain decomposition method for the modelisation of flow in 3D fracture networks

The major part of freshwater comes from sub-surface resources. Our work fits in a process to protect this vital resource, based on modelisation and numerical simulation. In conjunction with field studies, numerical simulations have to be used, due to the geological uncertainties. These uncertainties lead to stochastic modelisation. We concentrate on flow in fracture networks, randomly generated. To be able to solve those flow by a mixed hybrid finite elements method, we develop a meshing algorithm for the fractures. Then we are able to construct the linear systems, whatever the network randomly generated geometry. Then we compare three linear solvers : a direct solver, an algebraic multigrid and a Preconditioned Conjugate Gradient. This study leads us to propose a more efficient method, better suited to our problem solving. We study a domain decomposition method, which takes advantages from both the direct method and the Preconditioned Conjugate Gradient. This Schur method reduces the global problem to an interface problem, with a natural domain decomposition based on fractures or fracture packs. We propose an original approach for optimizing the algorithm and a global preconditioning of deflation type. Our implementation is efficient, since it succeeds to solve all the systems tested and is, in most cases, faster than the other linear solvers.