Adaptive mesh refinement with an enhanced velocity mixed finite element method on semi-structured grids using a fully coupled solver

We describe a novel approach for performing adaptive mesh refinement using mixed finite elements for flow in porous media applications. The enhanced velocity (EV) mixed finite element method is used to construct a strongly flux-continuous velocity approximation between non-matching subdomain grids. In this work, the original EV implementation was generalized to allow interfaces in the interior of subdomains adjacent to inactive cells and to allow dynamic adaptive mesh refinement (AMR). In the new implementation, subdomains with different spatial resolutions are stacked on top of each other to produce a very general semi-structured grid. The decomposition is non-overlapping, but now the subdomains can have holes, have ragged edges, and be nested within each other. Several examples with adaptive mesh refinement are demonstrated in two and three spatial dimensions; a priori indicators are used to adapt the grid for a multiphase compositional flow model, and a posteriori indicators are used to adapt the grid for a single-phase flow model. Moreover, a new fully coupled linear solver for the EV method is also implemented in this work, which shows a dramatic reduction in the number of Newton iterations versus the previously implemented nonlinear block Jacobi solver, especially when systems have a strong elliptic component.