An iterative multiscale finite volume algorithm converging to the exact solution

Lunati, Ivan; Tyagi, Manav; Lee, Seong H.

doi:10.1016/j.jcp.2010.11.036

Cited by 53 publications

(43 citation statements)

References 27 publications

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“…We refer to [29,30] for further details and for an extensive description of the construction of the conservative velocity field.…”

Section: The Msfv Methodsmentioning

confidence: 99%

“…Different strategies have been proposed to estimate the neglected transversal fluxes and improve the accuracy of the MsFV method [10,30]. Following [30], we construct an iterative scheme that uses the pressure residual, r À Ap, to estimate the transversal fluxes and combines the MsFV operator with a Krylov subspace accelerator.…”

Section: Iterative Improvement Of the Local Boundary Conditionsmentioning

confidence: 99%

“…Following [30], we construct an iterative scheme that uses the pressure residual, r À Ap, to estimate the transversal fluxes and combines the MsFV operator with a Krylov subspace accelerator. The resulting algorithm is equivalent to the preconditioned Richardson equation…”

Section: Iterative Improvement Of the Local Boundary Conditionsmentioning

confidence: 99%

“…where m denotes the pressure iteration level [30], and the Generalized Minimal Residual method (GMRES [36]) is used to compute the relaxation parameter x m .…”

Section: Iterative Improvement Of the Local Boundary Conditionsmentioning

confidence: 99%

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An adaptive multiscale method for density-driven instabilities

Künze

Lunati

2012

Journal of Computational Physics

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“…We refer to [29,30] for further details and for an extensive description of the construction of the conservative velocity field.…”

Section: The Msfv Methodsmentioning

confidence: 99%

Section: Iterative Improvement Of the Local Boundary Conditionsmentioning

confidence: 99%

Section: Iterative Improvement Of the Local Boundary Conditionsmentioning

confidence: 99%

“…where m denotes the pressure iteration level [30], and the Generalized Minimal Residual method (GMRES [36]) is used to compute the relaxation parameter x m .…”

Section: Iterative Improvement Of the Local Boundary Conditionsmentioning

confidence: 99%

See 2 more Smart Citations

An adaptive multiscale method for density-driven instabilities

Künze

Lunati

2012

Journal of Computational Physics

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“…Contrary to classical domain decomposition methods, MCDD will produce solutions that are mass conservative at any iteration step, thus it is not necessary to reduce the pressure residual to a very low value before solving transport equations. Various aspects of MCDD have been tested for two-dimensional problems (Kippe, et al, 2008;Sandvin, et al, 2011;Lunati, et al, 2011). However, to formulate multiscale methods for three-dimensional problems has turned out to be considerably more difficult in general, and to our knowledge, no applications of MCDDtype methods within an iterative setting have been reported in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Mass Conservative Domain Decomposition for Porous Media Flow

Nordbotten¹,

Keilegavlen²,

Sandvin³

2012

Finite Volume Method - Powerful Means of Engineering Design

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Physics-based preconditioners for flow in fractured porous media

2014

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Discrete fracture models are an attractive alternative to upscaled models for flow in fractured media, as they provide a more accurate representation of the flow characteristics. A major challenge in discrete fracture simulation is to overcome the large computational cost associated with resolving the individual fractures in large-scale simulations. In this work, two characteristics of the fractured porous media are utilized to construct efficient preconditioners for the discretized flow equations. First, the preconditioners are tailored to the fracture geometry and presumed flow properties so that the dominant features are well represented there. This assures good scalability of the preconditioners in terms of problem size and permeability contrast. For fracture dominated problems, numerical examples show that such geometric preconditioners are comparable or preferable when compared to state-of-the-art algebraic multigrid preconditioners. The robustness of the physics-based preconditioner for less favorable fracture conditions is further demonstrated by a systematic degradation of the fracture hierarchy. Second, the preconditioners are physics preserving in the sense that conservative fluxes can be computed even for an inexact pressure solutions. This facilitates a scheme where accuracy in the linear solver can be traded for efficiency by terminating the iterative solvers based on error estimates, and without sacrificing basic physical modeling principles. With the combination of these two properties a novel preconditioner is obtained which bridges the gap between multiscale approximations and iterative linear solvers.

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An iterative multiscale finite volume algorithm converging to the exact solution

Cited by 53 publications

References 27 publications

An adaptive multiscale method for density-driven instabilities

An adaptive multiscale method for density-driven instabilities

Mass Conservative Domain Decomposition for Porous Media Flow

Physics-based preconditioners for flow in fractured porous media

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