Accelerated non-linear finite volume method for diffusion

Vidović, D.; Dimkić, Milan; Pušić, M.

doi:10.1016/j.jcp.2011.01.016

Cited by 11 publications

(21 citation statements)

References 25 publications

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“…In a linear nite volume method, the coe cients ± are equal and xed while is zero [7]. On the other hand, in a non-linear nite volume method [14], + and − may be di erent and depend on the hydraulic head values in some cells other than ± .…”

Section: Discretizationmentioning

confidence: 99%

“…Let x be another collocation point. Based on (14), the di erence between the hydraulic head values at x and x + is…”

Section: Integrating (1) Over Cell Yieldsmentioning

confidence: 99%

“…The proposed scheme is used within the near-well region and scheme [14] is applied outside of this region. The near-well region can be of any shape, but it should include at least the cells nearest to the well.…”

Section: Integrating (1) Over Cell Yieldsmentioning

confidence: 99%

“…Non-linear two-point schemes [2,8,9,[13][14][15][16] were not originally formulated for the near-well discretization and thus loose their accuracy on coarse grids if a well is present. This type of scheme was adapted for well-driven ow through an isotropic medium in [6].…”

Section: Introductionmentioning

confidence: 99%

“…The rst correction (see Section 3.1) is applied only to well faces, while the uxes through other faces are approximated using the unmodi ed non-linear two-point scheme [14]. The resulting well extraction rate is improved in comparison with the uncorrected scheme on coarse meshes, but the hydraulic head is not second-order accurate near the well.…”

Section: Introductionmentioning

confidence: 99%

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Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media

Dotlić

2014

Computational Methods in Applied Mathematics

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We consider a nite volume method for ow simulations in an anisotropic porous medium in the presence of a well. The hydraulic head varies logarithmically and its gradient changes rapidly in the well vicinity. Thus, the use of standard numerical schemes results in a completely wrong total well ux and an inaccurate hydraulic head. In this article we propose two nite volume methods to model the well singularity in an anisotropic medium. The rst method signi cantly reduces the total well ux error, but the hydraulic head is still not even rst-order accurate. The second method gives a second-order accurate hydraulic head and at least rst-order accurate total well ux.

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Section: Discretizationmentioning

confidence: 99%

“…Let x be another collocation point. Based on (14), the di erence between the hydraulic head values at x and x + is…”

Section: Integrating (1) Over Cell Yieldsmentioning

confidence: 99%

Section: Integrating (1) Over Cell Yieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media

Dotlić

2014

Computational Methods in Applied Mathematics

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On the accuracy of a nonlinear finite volume method for the solution of diffusion problems using different interpolations strategies

Queiroz

Souza

Contreras

et al. 2013

Numerical Methods in Fluids

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SUMMARYIn this paper, we consider a nonlinear finite volume method to solve the steady‐state diffusion equation in nonhomogeneous and non‐isotropic media. The method is nonlinear even if the original problem is linear. In its original form, the scheme is monotone, because the coefficient matrix is monotone under certain assumptions and, as a consequence, whenever the analytic operator demands, it preserves the positivity of numerical solutions. On the other hand, the scheme is unable to reproduce piecewise linear solutions exactly. In order to recover this interesting feature, we use two different interpolation strategies. In this case, even though we are unable to prove monotonicity, we show some numerical evidences that the combined method has an improved behavior, producing second order accurate solutions, even for nonhomogeneous and strongly anisotropic media. Copyright © 2013 John Wiley & Sons, Ltd.

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A monotone nonlinear finite volume method for approximating diffusion operators on general meshes

Camier

Hermeline

2016

Numerical Meth Engineering

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Summary The basic principles of the discrete duality and nonlinear monotone finite volume methods are combined in order to obtain a new monotone nonlinear finite volume method for the approximation of diffusion operators on general meshes. Numerical results highlight both the second‐order accuracy of this method on general meshes and its capability to deal with challenging anisotropic diffusion problems on various computational domains. Copyright © 2016 John Wiley & Sons, Ltd.

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Accelerated non-linear finite volume method for diffusion

Cited by 11 publications

References 25 publications

Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media

Finite Volume Methods for Well-Driven Flows in Anisotropic Porous Media

On the accuracy of a nonlinear finite volume method for the solution of diffusion problems using different interpolations strategies

A monotone nonlinear finite volume method for approximating diffusion operators on general meshes

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