Mimetic finite differences for porous media applications
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We connect the Mimetic Finite Difference method (MFD) with the finite-volume two-point flux scheme (TPFA) for Voronoi meshes. The main effect is reducing the saddle-point system to a much smaller symmetric-positive definite matrix. In addition, the generalization allows MFD to seamlessly integrate with existing porous media modeling technology. The generalization also imparts the monotonicity property of the TPFA method on MFD. The connection is achieved by altering the consistency condition of the velocity bilinear operator. First-order convergence theory is presented as well as numerical results that support the claims. We demonstrate a methodology for using MFD in modeling fluid flow in fractures coupled with a reservoir. The method can be used for nonplanar fractures. We use the method to demonstrate the effects of fracture curvature on single-phase and multi-phase flows. Standard benchmarks are used to demonstrate the accuracy of the method. The approach is coupled with existing reservoir simulation technology.