M-Matrix Flux Splitting for General Full Tensor Discretization Operators on Structured and Unstructured Grids

Edwards, Michael G.

doi:10.1006/jcph.2000.6418

Cited by 75 publications

(112 citation statements)

References 21 publications

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“…The derivation of algebraic flux continuity conditions for full tensor discretization operators has lead to efficient and robust locally conservative flux continuous finite volume methods for determining the discrete velocity field in subsurface reservoirs e .g [1][2][3][4][5][6][7][8] .…”

Section: S Ummarymentioning

confidence: 99%

“…Consistent flux approximations that respect continuity in pressure and flux across the control-volume interfaces witkin each primal grid cell are presented in [4][5][6][7][8] . These scheures involve the introduction of auxiliary continuons interface pressures, one per control-volume sub-face as indicated in sub-triangle and flux continuity is imposed by equating fluxes on the lelt and right hand sides of each interface .…”

Section: Control-volume Flux and Continuity In Two Dimensionsmentioning

confidence: 99%

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Symmetric Positive Definite General Tensor Discretization Operators on Unstructured and Flow Based Grids

Edwards¹

2002

ECMOR VIII - 8th European Conference on the Mathematics of Oil Recovery

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Section: S Ummarymentioning

confidence: 99%

Section: Control-volume Flux and Continuity In Two Dimensionsmentioning

confidence: 99%

Symmetric Positive Definite General Tensor Discretization Operators on Unstructured and Flow Based Grids

Edwards¹

2002

ECMOR VIII - 8th European Conference on the Mathematics of Oil Recovery

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“…[2] suggested using the extended stencil only locally based on the importance of the local contribution from the non-7-pt gridblocks . Edwards [7] proposed operator splitting scheures for dealing with these wider stencils . He retains the two-point flux, which yields a 7-pt stencil, and a remainder .…”

Section: Linear Solvers For Multi-point Stenci Lmentioning

confidence: 99%

“…Edwards describes a general framework for his splitting scheme, and he applies it to structured and unstructured grids . [7,8] also showed that his splitting operator ponsessen many desirable properties . Using a variety of two-dimensional multiphase flow problems, he showed that his scheme converged to the feil matrix solution .…”

Section: Linear Solvers For Multi-point Stenci Lmentioning

confidence: 99%

“…We examined numerical algorithms to solve the resulting matrix efficiently . Following Edwards' work [7], we also investigated operator splitting scheures for the local problems . We compared the convergente rate of these 7-point preconditioners to find that all the iterative scheures based on the 7-point conditioners converge well .…”

Section: Discusion and Conclusion Smentioning

confidence: 99%

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A Black-Oil Reservoir Simulator for Hexahedral Multiblock Grids

Lee¹,

Jenny²,

Wolfsteiner³

2002

ECMOR VIII - 8th European Conference on the Mathematics of Oil Recovery

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A black oil reservoir simulator was developed for hexahedral minti-block grids . An objectoriented approach for the design and implementation of the simulator was adopted . We discuss the general features and object-oriented (0/0) design of the simulator.Complexity in geological or well features in a reservoir model (e .g., faults, inclined and multi-lateral wens) entails non-orthogonal and/or unstructured grids in place of conventional Cartesian grids . To obtain flexibility in gridding as well as numerical efficiency, hexahedral minti-block grids are employed . These multiblock are locally structured and globall y unstructured.In general, one can always generate multiblock grids with matched grids at block boundaries, and that leads to simple data structuren and communication patterns between blocks . Nevertheless, when geometrical boundaries (e .g. fault surfaces) become complex, multiblock grid with matched grids tends to create many blocks with small cells . We generalize the multiblock grid to the case where the gridlines do not match at block boundaries . The general quality and characteristics of multiblock grids, with matched or unmatched grids at the block boundaries, are discussed .Minti-point discretization scheures are necessary to accommodate non-orthogonal grid and tensor permeability . A flux-continuous finite difference scheme, which was previously developed for hexahedral grids with tensor permeability, is extended to multiblock systems with unmatched grids . We also present efficient iterative solution scheures that take advantage of the locally structured character of the computational grid .We demonstrate the capabilities of this generalized multiblock approach using examples of practical interest : (1) An SPE comparative study and (2) a real reservoir model with multiple complex faults and internal surfaces .

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Convergence study of a family of flux‐continuous, finite‐volume schemes for the general tensor pressure equation

Pal

Edwards

Lamb

2006

Numerical Methods in Fluids

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101

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SUMMARYIn this paper, a numerical convergence study of family of ux-continuous schemes is presented. The family of ux-continuous schemes is characterized in terms of quadrature parameterization, where the local position of continuity deÿnes the quadrature point and hence the family. A convergence study is carried out for the discretization in physical space and the e ect of a range of quadrature points on convergence is explored. Structured cell-centred and unstructured cell-vertex schemes are considered.Homogeneous and heterogeneous cases are tested, and convergence is established for a number of examples with discontinuous permeability tensor including a velocity ÿeld with singularity. Such cases frequently arise in subsurface ow modelling. A convergence comparison with CVFE is also presented.

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M-Matrix Flux Splitting for General Full Tensor Discretization Operators on Structured and Unstructured Grids

Cited by 75 publications

References 21 publications

Symmetric Positive Definite General Tensor Discretization Operators on Unstructured and Flow Based Grids

Symmetric Positive Definite General Tensor Discretization Operators on Unstructured and Flow Based Grids

A Black-Oil Reservoir Simulator for Hexahedral Multiblock Grids

Convergence study of a family of flux‐continuous, finite‐volume schemes for the general tensor pressure equation

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