Discretization on Non-Orthogonal, Quadrilateral Grids for Inhomogeneous, Anisotropic Media

Aavatsmark, Ivar; Barkve, T.; Bøe, Ø.; Mannseth, Trond

doi:10.1006/jcph.1996.0154

Cited by 217 publications

(215 citation statements)

References 13 publications

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“…An important aspect of coarsening is that K c becomes often anisotropic, even if the original hydraulic permeability K is isotropic. Recently, methods became available that cope with the off-diagonal components in a tensor [Aavatsmark et al, 1996;Lee et al, 1998;Anderman et al, 2002].…”

Section: Coarse-scale Equationsmentioning

confidence: 99%

Limitations to upscaling of groundwater flow models dominated by surface water interaction

Vermeulen

Stroet

Heemink

2006

Water Resources Research

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[1] Different upscaling methods for groundwater flow models are investigated. A suite of different upscaling methods is applied to several synthetic cases with structured and unstructured porous media. Although each of the methods applies best to one of the synthetic cases, no performance differences are formed if the methods were applied to a real three-dimensional case. Furthermore, we focus on boundary conditions, such as Dirichlet, Neumann, and Cauchy conditions, that characterize the interaction of groundwater with, for example, surface water and recharge. It follows that the inaccuracy of the flux exchange between boundary conditions on a fine scale and the hydraulic head on a coarse scale causes additional errors that are far more significant than the errors due to an incorrect upscaling of the heterogeneity itself. Whenever those errors were reduced, the upscaled model was improved by 70%. It thus follows that in practice, whenever we focus on predicting groundwater heads, it is more important to correctly upscale the boundary conditions than hydraulic transmissivity.

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Section: Coarse-scale Equationsmentioning

confidence: 99%

Limitations to upscaling of groundwater flow models dominated by surface water interaction

Vermeulen

Stroet

Heemink

2006

Water Resources Research

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“…The Gradient Discretization method (GDM) [5,3] provides a common mathematical framework for a number of numerical schemes dedicated to the approximation of elliptic or parabolic problems, linear or nonlinear, coupled or not; these include conforming and non conforming finite element, mixed finite element, hybrid mixed mimetic schemes [4] and some Multi-Point Flux Approximation [1] and Discrete Duality finite volume schemes [2] : we refer to [3, Part III] for more on this (note that in the present proceedings, it is shown that in some way the Discontinuous Galerkin schemes may also enter this framework [6]). Let us recall this framework in the case of the following linear elliptic problem:…”

Section: Introductionmentioning

confidence: 99%

An Error Estimate for the Approximation of Linear Parabolic Equations by the Gradient Discretization Method

Droniou

Eymard

Gallouët

et al. 2017

Springer Proceedings in Mathematics &Amp; Statistics

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We establish an error estimate for fully discrete time-space gradient schemes on a simple linear parabolic equation. This error estimate holds for all the schemes within the framework of the gradient discretisation method: conforming and non conforming finite element, mixed finite element, hybrid mixed mimetic family, some Multi-Point Flux approximation finite volume scheme and some discontinuous Galerkin schemes.

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“…In the more accurate multipoint flux approximation (MPFA), on the other hand, additional blocks are involved, which lead naturally to larger stencils than those in the TPFA methods. In 3D structured grids, for example, the MPFA method developed by [1] results in a 27-point stencil for the cellcentered pressure equations, compared with the sevenpoint stencils used in the TPFA methods. The approach has been studied by others as well [30,53].…”

Section: Introductionmentioning

confidence: 99%

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

Rasaei

Sahimi

2008

Comput Geosci

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We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs. The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological model. As such, the method is a multiscale one that preserves all the important information across all the relevant length scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly reduced computational cost. The speedup in the computations is up to over three orders of magnitude, depending on the degree of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and without the capillary pressure.

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Discretization on Non-Orthogonal, Quadrilateral Grids for Inhomogeneous, Anisotropic Media

Cited by 217 publications

References 13 publications

Limitations to upscaling of groundwater flow models dominated by surface water interaction

Limitations to upscaling of groundwater flow models dominated by surface water interaction

An Error Estimate for the Approximation of Linear Parabolic Equations by the Gradient Discretization Method

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

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