Analysis of a domain decomposition method for the coupling of Stokes and Darcy equations

By Marco Discacciati, Alfio Maria Quarteroni. 2003

116 citations recorded by the source corpus.

We introduce a differential system based on the coupling of the (Navier) Stokes equations and the Darcy equation for the modelling of the interaction between surface and subsurface flows. We formulate the problem as an interface problem and analyze the associated Steklov-Poincare operator. We then propose a way of solving the coupled problem iteratively, based on a suitable splitting of the interface conditions, allowing the solution of two subproblems at each step.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/de1aba3ebf46135d657facb115eca786088bc889

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

NON-MATCHING MORTAR DISCRETIZATION ANALYSIS FOR THE COUPLING STOKES-DARCY EQUATIONS (2007, background): “The differential systems are introduced in Section 3, where velocity and normal flux are considered as the boundary data for the Stokes part and the Darcy part , respectively; for other formulations and boundary data see [11, 12].”
Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition (2010, methodology): “decomposition method [1, 2, 3, 4], using the Lagrange multiplier approach [5, 6], or the two-grid method [7].”
Combining a level‐set method and a mixed stabilized P1/P1 formulation for coupling Stokes–Darcy flows (2012, methodology): “Generally, in the literature a standard mixed formulation is used to solve the Stokes equations while several approaches can be used to solve the Darcy equations, including a mixed formulation [7–9] and a standard variational formulation of Poisson’s equation [10].”
A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow (2007, unknown): “Keywords Porous media flow, Stokes equations, Darcy’s law, Multi-modeling prob- lems, Two-grid method.”
Navier-Stokes/Darcy Coupling: Modeling, Analysis, and Numerical Approximation (2009, methodology): “Under these conditions, the analysis of the coupled Stokes/Darcy problem has been studied in [40, 49, 53, 55, 56, 68, 69, 70, 71, 72, 88, 112, 113] in the steady case, and in [43, 124] in the time-dependent case.”
Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations (2004, methodology): “A description of other boundary conditions of physical relevance can be found in [6].”
Computational issues related to iterative coupling of subsurface and channel flows (2007, methodology): “Numerical studies focused on coupling Darcy flow with shallow water equations [3,4], and on coupling Darcy and Stokes flows in 2D [5,6] as well as in 3D [12].”
Time-dependent coupling of Navier–Stokes and Darcy flows (2013, methodology): “Furthermore, it has the advantage of being independent of the Steklov-Poincaré operator used in [16, 19, 20] that does not seem to apply to rough interfaces.”
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]).”
Mathematical and numerical models for coupling surface and groundwater flows (2002, background): “In its turn, S h can be split as sum of two operators S and S ph , associated to the subproblems (30) and (31) respectively The following theorem holds (see [6]) is with respect to h .”