Higher‐resolution hyperbolic‐coupled‐elliptic flux‐continuous CVD schemes on structured and unstructured grids in 2‐D

Abstract

SUMMARYHigher-order convection schemes have been developed for the essentially hyperbolic systems of reservoir simulation and can significantly enhance solution quality. Locally conservative full-tensor flux-continuous finite-volume schemes have also been developed for the porous medium pressure equation with general geometry and permeability tensors on structured and unstructured grids. These schemes remove O(1) errors induced by standard methods, and are now recognized as an essential component of any numerical method designed for reservoir simulation and modelling flow in porous media.In this paper, novel higher-resolution hyperbolic conservation law schemes, designed for convective flux approximation on unstructured grids are coupled with general full-tensor continuous Darcy flux approximations. The schemes are developed for multi-phase flow in porous media. Benefits in terms of improved front resolution are demonstrated. Comparisons with current methods including the controlvolume finite element (CVFE) method highlight the advantages of the new formulation for flow resolution in reservoir simulation.

Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance

“…The schemes employed here have been designed to overcome the TPFA limitations and involve families of control-volume distributed multi-point flux approximations (CVD-MPFA), with flow variables and rock properties being controlvolume distributed and assigned to share the same controlvolume locations. Both cell-vertex and cell-centred CVD-MPFA formulations [19][20][21][22][23][24][25][26][27][28] are compared in this work on unstructured grids. Related cell-centred MPFA methods are presented in [1-3, 44, 48, 80].…”

Global and local central non‐upwind finite volume schemes for hyperbolic conservation laws in porous media

“…Higher-order upwind approximations have also been developed [2][3][4][5][6][7][8][9][10]. Higher-order unstructured methods for flow in porous media are presented in [11][12][13].…”

Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids

“…The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) [6] coupled with a higher resolution approximation for convective transport [1,5]. The symmetric CVD-MPFA method is used for Darcy-flux approximation including pressure, gravity, and capillary pressure flux components.…”