Time: |
December 17, 2013 |
Lecturer: |
Prof. Dr. Jan Nordbotten
Department of Mathematics, University of Bergen, Norway |
Venue: |
Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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The development of cell-centered finite volume discretizations for deformation is motivated by the desire for a compatible approach with the discretization of fluid flow in deformable porous media. We express the conservation of momentum in the finite volume sense, and introduce three approximations methods for the cell-face stresses. The discretization method is developed for general grids in one to three spatial dimensions, and leads to a global discrete system of equations for the displacement vector in each cell, after which the stresses are calculated based on a local expression. The method allows for anisotropic, heterogeneous and discontinuous coefficients.We validate the method through numerical convergence tests. Furthermore, we highlight the flexibility of the method through applications to Biot's equations in soils and tissues, and to fractured media.