Coupling Fluid Flow with Porous Media Flow

By William J. Layton, Friedhelm Schieweck, Ivan Yotov. SIAM Journal on Numerical Analysis, 2002

599 citations recorded by the source corpus.

Subfields: Computational Mechanics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/433f25efa8cfe8b3961e2d6e65a370777f104b84

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In Computational Mechanics

In Environmental Engineering

Citations in the corpus

Computational issues related to iterative coupling of subsurface and channel flows (2007, methodology): “In [9], Layton, Schieweck and Yotov provide a variational formulation for which weak solutions are shown to exist and which can be used as a base for a domain decomposition strategy”
NON-MATCHING MORTAR DISCRETIZATION ANALYSIS FOR THE COUPLING STOKES-DARCY EQUATIONS (2007, methodology): “In [20], Layton, Schieweck, and Yotov developed existence and uniqueness of the weak solution for this problem.”
Mortar finite element discretization of a model coupling Darcy and Stokes equations (2008, background): “Note that a lot of recent works deal with the coupling of Darcy and Stokes equations in different frameworks, hence with other types of matching conditions such as the Beaver-Joseph-Saffman conditions, see [10,16,21,23,28,35] and the references therein.”
A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium (2007, methodology): “[19] use a Lagrange multiplier on the interface Γ to both aid in the approximation of the Beavers-Joseph-Saffman boundary condition and to allow the use of existing Darcy and Stokes flow simulators in a domain-decomposition (Ωd and Ωs) iterative technique.”
Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation (2009, methodology): “We point out that the conditions studied by Jäger and Mikelić have been adopted also in [88, 113, 40].”
UNIFORMLY-STABLE FINITE ELEMENT METHODS FOR DARCY-STOKES-BRINKMAN MODELS (2008, background): “In addition, the source term g is assumed to satisfy the solvability condition: ∫ Ω gdx = 0.”
Two‐phase flows in karstic geometry (2014, methodology): “The last velocity interface boundary condition is exactly the Beavers-Joseph-Saffman-Jones interface boundary condition [10, 12, 14, 15, 60, 61, 62, 63, 64, 65] with the slip coefficient β equal to the Beavers-Joseph-Saffman-Jones coefficient αBJSJ .”
Weak Galerkin method for the coupled Darcy-Stokes flow (2014, methodology): “In [26], Layton, Schieweck and Yotov has proved the equivalence between (2.”
Asymptotic analysis of the differences between the Stokes–Darcy system with different interface conditions and the Stokes–Brinkman system☆ (2010, background): “Consequently, many simplified versions of this interface conditions have emerged, among which the Beavers-Joseph-Saffman-Jones interface condition [12, 13, 16] is widely used; in this condition, the contribution of the tangential velocity in the porous media is neglected.”
A discretization and multigrid solver for a Darcy–Stokes system of three dimensional vuggy porous media (2009, methodology): “We rewrite the system as a variational problem (for more details, the interested reader may consult, e.g., [2, 4, 20 ]).”
Topology optimization of creeping fluid flows using a Darcy–Stokes finite element (2006, background): “This leads to challenges in determining approximating function spaces that yield unified numerical stability of both flow models [20, 21].”
DG Approximation of Coupled Navier-Stokes and Darcy Equations by Beaver-Joseph-Saffman Interface Condition (2009, methodology): “Similar interface conditions were considered in the coupling of the linear equations of Stokes and Darcy (see [25, 16, 17, 30, 28, 29]).”
Convergence of a family of Galerkin discretizations for the Stokes–Darcy coupled problem (2011, methodology): “Following [5,8] (see also [4]), one usually considers the homogeneous Neumann condition: u2 · ν = 0 on , (2.”
Navier–Stokes/Forchheimer models for filtration through porous media (2013, methodology): “Under those conditions, the analysis of a coupled Stokes/Darcy problem has been studied in [10,17,19,20,28,29,26,27,30,40,48] in the steady case, and in [12,53] in the time-dependent case.”