Consisitent and Accurate Finite Volume Methods for Coupled Flow and Geomechanics

Tuesday, 16 December 2014
Jan M Nordbotten, University of Bergen, Bergen, Norway; Princeton University, Civil and Environmental Engineering, Princeton, NJ, United States
We introduce a new class of cell-centered finite volume methods for elasticity and poro-elasticity. As compared to lowest-order finite element discretizations, the new discretization has no additional degrees of freedom, and yet gives more accurate stress and flow fields. This finite volume discretization methods has furthermore the advantage that the mechanical discretization is fully compatible (in terms of grid and variables) with the standard cell-centered finite volume discretizations that are prevailing for commercial simulation of multi-phase flows in porous media. 
Theoretical analysis proves the convergence of the method. We give results showing that so-called numerical locking is avoided for a large class of structured and unstructured grids. The results are valid in both two and three spatial dimensions. 
The talk concludes with applications to problems with coupled multi-phase flow, transport and deformation, together with fractured porous media.