... in flow simulations has been the objective of numerous consistent discretization methods that include mixed finite element (MFE) methods ( Russell and Wheeler 1983 ), multi-point flux approximation (MPFA) methods ( Aavatsmark et al. 1996 ; Edwards and Rogers 1998 ), nonlinear two-point flux approximation...

... Abstract A novel discrete fracture model (DFM) approximation is presented and coupled with the control-volume distributed multi-point flux approximation (CVD-MPFA) formulation. The reduced-dimensional discrete discontinuous pressure model for intersecting fractures is extended to two-phase flow...

... Abstract A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection...

... Abstract A three-dimensional symmetric positive definite (SPD) cell-centred control-volume distributed multi-point flux approximation (CVD-MPFA) is presented for porous media flow simulation on tetrahedral grids. The scheme depends on a single degree of freedom per control-volume and is derived...

... that is grid and geometry dependent. Families of locally conservative cell-based multidimensional upwind schemes that reduce both directional and crosswind diffusion are presented for convective flow approximation in porous media. The schemes are coupled with full-tensor Darcy flux approximations and handle...

... Abstract In the last decade, the multi-point flux approximations have found significant interest. However, non-physical oscillations can appear in the developed multi-point flux approximations when the anisotropy is really strong. It has been found that the oscillations are closely related...

... technique and an adaptive local-global procedure based on two-point flux approximations – applied individually. The extension of the VCMP-ALG method to irregular quadrilateral grids is also accomplished. Finally, we present results for two-phase oil-water flows, for which the models based on the VCMP-ALG...

... Abstract We present a multi-point flux approximation (MPFA) scheme for simulation of 3-D multi-phase flow on adapted grids. It is an extension of the VCMP (Variable Compact Multi-Point) scheme, which constructs stencils that are locally adapted to flow through transmissibility upscaling...

... a i , j is assembled from transmissibility coefficients as: Abstract This paper investigates the control volume method with multipoint flux approximation (MPFA) applied to the discetization of –div( K ( x )grad u ) = f ( x ), the equation describing fluid flow through anisotropic porous...

... Abstract Multi-point flux approximations (MPFAs) have been developed in recent years to improve the accuracy of the flux computation for reservoir simulation when the reservoir grids are not K-orthogonal. Recent studies, however, have shown that commonly used MPFA approaches could pose severe...

... control volume finite difference technique with a two-point flux approximation. The implementation is generally compatible with any simulator that represents grid connections via a connectivity list. A specialized treatment based on a "star-delta" transformation is introduced to eliminate control volumes...

... Abstract Standard simulators that can only allow for a diagonal tensor routinely perform simulations with O(1) errors in the velocity field whenever a full tensor is present. Two approaches that permit the use of diagonal tensor 2-point flux approximations are either (a) to only employ K...

... n → d the outward normal to the interface A i , j d ( Fig. 3 ) Let Q i , j d be the flux approximation over interface A i , j d i.e., Q i , j d ≃ ∫ A i , j d ( K ˜ λ n ∇ → P n + 1...