A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

Friis, Helmer André; Edwards, Michael G.

doi:10.1016/j.jcp.2010.09.012

Cited by 58 publications

(69 citation statements)

References 40 publications

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“…Prior to the solution process, the auxiliary pressures are expressed algebraically in terms of the primal pressures via the local flux continuity conditions and lead to a locally conservative formulation with continuous fluxes only dependent on primal pressures. Both cell-centred and vertex-centred CVD-MPFA approximations are considered in this work [19,20,[22][23][24][25][26][27][28]. A comparison between cell-centred and vertex-centred CVD-MPFA schemes is presented here, in terms of computed flow fields resulting from the respective pressure equation approximations.…”

Section: Pressure Equationmentioning

confidence: 99%

“…The cell-centred and cell-vertex CVD-MPFA formulations involve multiple families of schemes defined by the local flux quadrature point parameterization on each control-volume face [25,28]. A single family is parameterized by a dimensionless variable q.…”

Section: Pressure Equationmentioning

confidence: 99%

“…For a given grid type, there are two basic types of CVD-MPFA formulation determined by the choice of basis functions: (a) triangle pressure support (TPS) with linear basis functions over subcell triangles leading to pointwise pressure continuity on control-volume sub-faces [19,20,23,24]; (b) full pressure support (FPS) with subcell bilinear basis functions, leading to full pressure continuity over control-volume sub-faces [22,25,28].…”

Section: Pressure Equationmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

“…In the next section, description of the grid generation techniques together with generation of BAGs and WAGs is presented. This is followed by a brief description of the control-volume distributed multipoint flux approximation (CVD-MPFA) schemes, including the earlier piecewise-linear based formulations [19,20,23,24], and more robust piecewise-bilinear based formulations [22,25,27,28]. A comparison between the cell-centred and cell-vertex CVD-MPFA results and corresponding grids is presented, followed by conclusions.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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Grid generation for reservoir simulation must honor classical key constraints and be boundary aligned such that control-volume boundaries are aligned with geological features such as layers, shale barriers, fractures, faults, pinch-outs, and multilateral wells. An unstructured grid generation procedure is proposed that automates control-volume and/or control point boundary alignment and yields a PEBI-mesh both with respect to primal and dual (essentially PEBI) cells. In order to honor geological features in the primal configuration, we introduce the idea of protection circles, and to generate a dual-cell feature based grid, we construct halos around key geological features. The grids generated are employed to study comparative performance of cell-centred versus cell-vertex control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent degrees of freedom. The formulation of CVD-MPFA schemes in cellcentred and cell-vertex modes is analogous and requires switching control volume from primal to dual or vice versa together with appropriate data structures and boundaryThe original version of this article was revised: Due to an oversight, some author's corrections were not carried out during Performing proof corrections stage. The Publisher apologizes for these mistakes. conditions. The relative benefits of both types of approximation, i.e., cell-centred versus vertex-centred, are made clear in terms of flow resolution and degrees of freedom required.

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Section: Pressure Equationmentioning

confidence: 99%

Section: Pressure Equationmentioning

confidence: 99%

Section: Pressure Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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A monotone finite volume scheme for advection–diffusion equations on distorted meshes

Wang

Yuan

et al. 2011

Numerical Methods in Fluids

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SUMMARY A new monotone finite volume method with second‐order accuracy is presented for the steady‐state advection–diffusion equation. The method uses a nonlinear approximation for both diffusive and advective fluxes that guarantee the positivity of the numerical solution. The approximation of the diffusive flux is based on nonlinear two‐point approximation, and the approximation of the advective flux is based on the second‐order upwind method with proper slope limiter. The second‐order convergence rate for concentration and the monotonicity of the nonlinear finite volume method are verified with numerical experiments. Copyright © 2011 John Wiley & Sons, Ltd.

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A family of multi‐point flux approximation schemes for general element types in two and three dimensions with convergence performance

Pal

Edwards

2011

Numerical Methods in Fluids

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SUMMARY A family of flux‐continuous, locally conservative, control‐volume‐distributed multi‐point flux approximation (CVD‐MPFA) schemes has been developed for solving the general geometry‐permeability tensor pressure equation on structured and unstructured grids. These schemes are applicable to the full‐tensor pressure equation with generally discontinuous coefficients and remove the O(1) errors introduced by standard reservoir simulation schemes when applied to full‐tensor flow approximation. The family of flux‐continuous schemes is characterized by a quadrature parameterization. Improved numerical convergence for the family of CVD‐MPFA schemes using the quadrature parameterization has been observed for structured and unstructured grids in two dimensions. The CVD‐MPFA family cell‐vertex formulation is extended to classical general element types in 3‐D including prisms, pyramids, hexahedra and tetrahedra. A numerical convergence study of the CVD‐MPFA schemes on general unstructured grids comprising of triangular elements in 2‐D and prismatic, pyramidal, hexahedral and tetrahedral shape elements in 3‐D is presented. Copyright © 2011 John Wiley & Sons, Ltd.

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A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

Cited by 58 publications

References 40 publications

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

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

A monotone finite volume scheme for advection–diffusion equations on distorted meshes

A family of multi‐point flux approximation schemes for general element types in two and three dimensions with convergence performance

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