q-Families of CVD(MPFA) Schemes on General Elements: Numerical Convergence and the Maximum Principle

Pal, Mayur; Edwards, Michael G.

doi:10.1007/s11831-010-9043-4

Cited by 18 publications

(21 citation statements)

References 46 publications

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“…Quadrature selection and implementation of CVD-MPFA Control-volume distributed(CVD) flux approximation schemes are implemented here, both in cell-centred and cell-vertex frameworks following the TPS formulations of [19,20,23,24], and the more robust FPS formulations [22,25,27,28]. The families of CVD-MPFA schemes are defined by the choice of quadrature points.…”

Section: Duality Of Cell-centred and Vertex-centred Methodsmentioning

confidence: 99%

“…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%

“…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: Duality Of Cell-centred and Vertex-centred Methodsmentioning

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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Finite analytic method for 2D steady fluid flows in heterogeneous porous media with unstructured grids

Wang

Liu

Wang

2017

Numerical Meth Engineering

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The finite analytic method (FAM) is developed to solve the 2D steady fluid flows in heterogeneous porous media with full tensor permeability on unstructured grids. The proposed FAM is constructed based upon the power‐law analytic nodal solution in the angular domain with arbitrary shape. When approaching the grid node joining the subdomains, 3 different flow patterns may exist: power‐law flow, linear flow, or the stagnant flow. Based on the nodal analytic solution, the triangle‐based FAM is proposed. Numerical examples show that the proposed numerical scheme makes the convergences much quickly than the traditional methods, typically the weighted harmonic mean method under the cell refinement. In practical applications, the grid refinement parameter n = 2 or n = 3 is recommended, and the relative error of the calculated equivalent permeability will below 4% independent of the heterogeneity. In contrast, when using the traditional numerical scheme the refinement ratio for the grid cell needs to increase dramatically to get an accurate result, especially for strong heterogeneous porous medium.

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Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

Wang

Liu

et al. 2017

Numerical Methods Partial

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The finite analytic numerical method for 3D quasi‐Laplace equation with conductivity in full tensor form is constructed in this article. For cubic grid system, the gradient of the potential variable will diverge when tending to the common edge joining the four grids with different conductivities. However, the potential gradient along the tangential direction is of limited value. As a consequence, the 3D quasi‐Laplace equations will behave as a quasi‐2D one. An approximate analytical solution of the 3D quasi‐Laplace equation can be found around the common edge, which is expressed as a combination of a power‐law function and a linear function. With the help of this approximate analytical solution, a 3D finite analytical numerical scheme is then constructed. Numerical examples show that the proposed numerical scheme can provide rather accurate solutions only with 3 × 3 × 3 or 4 × 4 × 4 subdivisions. More important, the convergent speed of the numerical scheme is independent of the conductivity heterogeneity. In contrast, when using the traditional numerical schemes, typically such as the MPFA method, the refinement ratio for the grid cell needs to increase dramatically to get an accurate result for the strong heterogeneous case.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1475–1492, 2017

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q-Families of CVD(MPFA) Schemes on General Elements: Numerical Convergence and the Maximum Principle

Cited by 18 publications

References 46 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

Finite analytic method for 2D steady fluid flows in heterogeneous porous media with unstructured grids

Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

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