January 27, 2015
||Prof. Oliver Sander
Department of Mathematics, IGPM, RWTH Aachen, Germany
||Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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We consider the mechanics of a macroscopic fracture in a poroelasticmedium. The medium is modelled as a linear Biot material, while the fractureappears as a discontinuity in the displacement field. The fracture is filledwith a fluid, which interacts both with the fluid and the rock matrix of theporoelastic medium. Under a pressure load on the fluid in the fracture,the fracture opens.In nature, fracture opening is counteracted upon by the weight of the rockmatrix above the fracture. To prevent mutual penetration of the two fracturesides, we discuss a model equipped with a contact condition. The resulting discretevariational inequality can be solved efficiently with a Truncated NonsmoothMultigrid (TNNMG) Solver. We show discretization error estimates for thecorresponding XFEM discretization.We simulate the coupled system using finite elements on two grids of differentdimensions. For the Biot solid we use a fixed grid and the extended finiteelement method (XFEM) for the displacement discontinuity. The fluid flow inthe fracture is modelled on a lower-dimensional grid nonconformingly embeddedinto the matrix grid. We briefly present FoamGrid, a Dune grid implementationdedicated to lower-dimensional fracture networks. The network and bulk gridsare coupled using the generic grid coupling mechanism available in the Dunegrid-glue library.