A mixed hybrid Mortar method for solving flow in discrete fracture networks

Abstract

We consider flow in discrete fracture networks made of 2D domains in intersection and solved with a mixed hybrid finite element method (MHFEM). The discretization within each fracture is performed in two steps: first, borders and intersections are discretized, second, based on these discretizations, a 2D mesh is built. Independent meshing process within each subdomain is of interest for practical use since it makes it easier to refine the chosen subdomains and to perform parallel computation. This article shows how MHFEM is well adapted for integrating a Mortar method to enforce the continuity of the fluxes and heads at the non-matching grids. Some numerical simulations are given to show the efficiency of the method in the case of a preferential orientation of the fractures where a comparison with the 2D solution is possible.

Keywords:

• mixed hybrid finite element method
• Mortar method
• fractured media

AMS Subject Classifications:

• 65N30
• 65N55
• 65N22

Acknowledgements

We sincerely wish to thank the reviewers for their constructive comments. This work was supported by the French National Research Agency, with the ANR-07-CIS-004 project MICAS.