On The Interface Boundary Condition of Beavers, Joseph, and Saffman

By Andro Mikelić, Willi Jäger. SIAM Journal on Applied Mathematics, 2000

473 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/213f82d29d7df65d9e328cfd5ec41957c6185c00

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In Biomedical Engineering

In Computational Mechanics

Citations in the corpus

Weak Galerkin method for the coupled Darcy-Stokes flow (2014, methodology): “In this paper, we consider the Beavers-Joseph-Saffman (BJS) interface condition [38, 21, 22, 23, 34], which is easier to handle than the original Beavers-Joseph interface condition [2], as the BJS condition will generate a coercive bilinear form in the variational formulation.”
Coupling Fluid Flow with Porous Media Flow (2002, background): “This leads to mathematical difficulties arising from the coupled system of equations of different orders in different regions.”
Analysis of the coupled Navier–Stokes/Biot problem (2017, background): “condition [4, 30, 22] which assumes that the tangential stress of the fluid is proportional to the slip rate.”
Computational issues related to iterative coupling of subsurface and channel flows (2007, background): “The third interface condition is the Beavers-Joseph relation [2,8]: the difference between the slip velocity of the free fluid u1 · τj and the tangential component of the seepage velocity u2 · τj was proposed to be proportional to the shear rate of the free fluid:”
Homogenization of a Darcy–Stokes system modeling vuggy porous media (2006, unknown): “Saffman [24] justified this law theoretically and showed that the term involving Ud could be dropped (see also [15, 16]).”
Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition (2010, methodology): “The simplified interface condition was mathematically validated by Jäger and Mikelic̀ [11] in the sense that the leading order interface boundary condition is the Beavers-Joseph-SaffmanJones boundary condition in the zero permeability limit under the similar assumptions as in Saffman’s work plus the”
Boundary Conditions at Fluid-Permeable Interfaces in Porous Media: a Variational Approach (2009, background): “Several authors (see e.g. Ochoa-Tapia and Whitaker (1995a), Jager and Mikelic (2000); Ochoa-Tapia and Whitaker (1995b); Hassanizadeh and Gray (1989)) formulated different boundary conditions to be used at solid material interfaces separating porous media and pure fluid.”
Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations (2004, background): “Conditions (3) impose the continuity of the normal velocity on Γ, as well as that of the normal component of the normal stress, but they allow pressure to be discontinuous across the interface (see [13, 8, 9]).”
Mathematical and numerical models for coupling surface and groundwater flows (2002, background): “Now it can be easily seen that upon setting n ( 0 , 0 , 1 ) (6), conditions (6) 1 and (6) 3 reduce 1 3 2 2 Finally allow the pressure to be discontinuous across the interface Γ , as advocated also by Jäger and Mikeli´c (see [8,9]).”