Geological media exhibit permeability fields and porosities that differ by several orders of magnitude across highly varying length scales. Computational methods used to model flow through such media should be capable of treating rough coefficients and grids. Further, the adherence of these methods to basic physical properties such as local mass balance and continuity of fluxes is of great importance. Both discontinuous Galerkin (DG) and mixed finite element (MFE) methods satisfy local mass balance and can accurately treat rough coefficients and grids. The appropriate choice of physical models and numerical methods can substantially reduce computational cost with no loss of accuracy. MFE is popular due to its accurate approximation of both pressure and flux but is limited to relatively structured grids. On the other hand, DG supports higher order local approximations, is robust and handles unstructured grids, but is very expensive because of the number of unknowns. To this end, we present DG-DG and DG-MFE domain decomposition couplings for slightly compressible single phase flow in porous media. Mortar finite elements are used to impose weak continuity of fluxes and pressures on the interfaces. The sub-domain grids can be non-matching and the mortar grid can be much coarser making this a multiscale method. The resulting nonlinear algebraic system is solved via a non-overlapping domain decomposition algorithm, which reduces the global problem to an interface problem for the pressures. Solutions of numerical experiments performed on simple test cases are first presented to validate the method. Then, additional results of some challenging problems in reservoir simulation are shown to motivate the future application of the theory.


Article metrics loading...

Loading full text...

Full text loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error