On boundary conditions for fluid flow in porous media

Lévy, T.; Sanchez‐Palencia, E.

doi:10.1016/0020-7225(75)90054-3

Cited by 119 publications

(85 citation statements)

References 11 publications

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“…At the interface between Darcy and NS domain, an interface parameter must be specified which honors the continuity of mass and momentum over the interface. For the Darcy-NS system, various interface conditions have been presented in some paper [22][23][24]. They differ in terms of treatment of jump of tangential component of the velocities across the interface.…”

Section: Governing Equationsmentioning

confidence: 99%

A three-dimensional model for negative half cell of the vanadium redox flow battery

Zhang

Xing

2011

Electrochimica Acta

171

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Section: Governing Equationsmentioning

confidence: 99%

A three-dimensional model for negative half cell of the vanadium redox flow battery

Zhang

Xing

2011

Electrochimica Acta

171

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“…Starting from the original experimental works of Beavers and Joseph on the coupling conditions between a fluid and a porous medium, mathematical investigations have been carried out in [66,83,84,85,89,95].…”

Section: Draft --Draft --Draft --Draft --Draft -M Discacciati/a Quamentioning

confidence: 99%

Navier-Stokes/darcy coupling: modeling, analysis, and numerical approximation

2009

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“…Appropriate interface conditions are based on the principles of mass conservation, equilibrium of normal stresses across the interface, and a special condition called the BeaversJoseph-Saffman condition [29,42] describing the relation between the shear stress and the tangential velocity. Many researchers have studied multiphysics problems theoretically; see, for example, [2,13,33,27].…”

Section: Introductionmentioning

confidence: 99%

Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System

Luo¹,

Rodrigo²,

Gaspar³

et al. 2017

SIAM J. Sci. Comput.

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Abstract. The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, local Fourier analysis is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs very well for small values of the hydraulic conductivity and fluid viscosity, which are relevant for applications.

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On boundary conditions for fluid flow in porous media

Cited by 119 publications

References 11 publications

A three-dimensional model for negative half cell of the vanadium redox flow battery

A three-dimensional model for negative half cell of the vanadium redox flow battery

Navier-Stokes/darcy coupling: modeling, analysis, and numerical approximation

Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System

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