Boundary Aligned Grid Generation and CVD-MPFA - Cell-centred Versus Cell-vertex on Unstructured Grids

Abstract

Development of boundary aligned grid generation is presented together with comparative performance of cell-vertex versus cell-centred CVD-MPFA finite-volume formulations using equivalent degrees of freedom. When generating structured or unstructured grids for reservoir simulation, classical key constraints involve boundary aligned grid generation with control-volume boundaries aligned with solid walls and geological features such as layers, shale barriers, fractures, faults, pinchouts and multilateral wells. The schemes used are control-volume distributed (CVD) with flow variables and rock properties sharing the same control-volume location and are comprised of a multipoint flux family formulation (CVD-MPFA). Consequently a natural choice is for primal grid cells to act as control-volumes, then grid generation can be performed with primal grid cell boundaries being aligned with key interior constraint boundaries. This naturally leads to cell-centred approximation, where flow variables and rock properties are associated with grid cell centres. The alternative is to employ cell-vertex approximation which uses far fewer approximation points on a given unstructured grid. In this case control-volumes are constructed around primal grid vertices. The grid generation process is less straight forward since control-volumes must be constrained to satisfy interior boundary alignment. A novel grid generation procedure is proposed that automates control-volume boundary alignment and yields a Voronoi mesh. The actual grid is then generated such that dual boundaries are aligned with key internal constraint boundaries and cell-vertex approximation becomes the natural choice. In this case flow variables and rock properties are associated with grid cell vertices and their dual control-volumes. The relative benefits of both types of approximation is made clear in terms of flow resolution and degrees of freedom required.