A finite volume method for approximating 3D diffusion operators on general meshes

Hermeline, F.

doi:10.1016/j.jcp.2009.05.002

Cited by 56 publications

(80 citation statements)

References 43 publications

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“…The DDFV scheme, see [9,15,26] for the two dimensional case and [7,8,11,13,14,27,28] for the three dimensional case, may also be seen as a gradient scheme. Consider the case where the domain Ω is the union of octahedra which are the so-called diamond cells (such a cell is depicted in Fig.…”

Section: Examplesmentioning

confidence: 99%

Small-stencil 3D schemes for diffusive flows in porous media

Eymard¹,

Guichard²,

Herbin³

2011

ESAIM: M2AN

149

184

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Abstract. In this paper, we study some discretization schemes for diffusive flows in heterogeneous anisotropic porous media. We first introduce the notion of gradient scheme, and show that several existing schemes fall into this framework. Then, we construct two new gradient schemes which have the advantage of a small stencil. Numerical results obtained for real reservoir meshes show the efficiency of the new schemes, compared to existing ones.

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Section: Examplesmentioning

confidence: 99%

Small-stencil 3D schemes for diffusive flows in porous media

Eymard¹,

Guichard²,

Herbin³

2011

ESAIM: M2AN

149

184

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“…(1.1) on both the primal and dual control volumes. In [8,23,2,18], each diamond cell is composed of a pair of pyramids having…”

Section: Nonlinear Elliptic Equationsmentioning

confidence: 99%

“…x a (d) 3D node control volume from [2,18]. as base an interface of the primal mesh and vertices the two neighboring centers (see figure 1.1(b)).…”

Section: Nonlinear Elliptic Equationsmentioning

confidence: 99%

A 3D Discrete Duality Finite Volume Method for Nonlinear Elliptic Equations

Coudière¹,

Hubert²

2011

SIAM J. Sci. Comput.

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Abstract. Discrete Duality Finite Volume (DDFV) schemes have recently been developed in 2D to approximate nonlinear diffusion problems on general meshes. In this paper, a 3D extension of these schemes is proposed. The construction of this extension is detailed and its main properties are proved: a priori bounds, well-posedness and error estimates. The practical implementation of this scheme is easy. Numerical experiments are presented to illustrate its good behavior.

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“…The first formulation to appear is based on interface flux computations for primary and dual meshes, accounting with the interface f lux continuity. The pioneer works for this formulation are [31] and [21] followed by [20,27,30,32] and [19]. The second formulation of DDFV is based on pressure gradient reconstructions over a diamond grid.…”

Section: Introduction and The Model Problemmentioning

confidence: 99%

Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems

2013

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This work presents and analyzes, on unstructured grids, a discrete duality finite volume method (DDFV method for short) for 2D-flow problems in nonhomogeneous anisotropic porous media. The derivation of a symmetric discrete problem is established. The existence and uniqueness of a solution to this discrete problem are shown via the positive definiteness of its associated matrix. Properties of this matrix combined with adequate assumptions on data allow to define a discrete energy norm. Stability and error estimate results are proven with respect to this norm. L 2 -error estimates follow from a discrete Poincaré inequality and an L ∞ -error estimate is given for a P 1 -DDFV solution. Numerical tests and comparison with other schemes (especially those from FVCA5 benchmark) are provided.A. Njifenjou (B) · I. Moukouop-Nguena

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A finite volume method for approximating 3D diffusion operators on general meshes

Cited by 56 publications

References 43 publications

Small-stencil 3D schemes for diffusive flows in porous media

Small-stencil 3D schemes for diffusive flows in porous media

A 3D Discrete Duality Finite Volume Method for Nonlinear Elliptic Equations

Analysis on general meshes of a discrete duality finite volume method for subsurface flow problems

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