Mathematical and numerical models for coupling surface and groundwater flows

By Marco Discacciati, E. Miglio, Alfio Maria Quarteroni. 2002

479 citations recorded by the source corpus.

In this paper we present some results about the coupling of Navier-Stokes and Shallow Water equations for surface flows and Darcy's equation for groundwater flows. We discuss suitable interface conditions and show the well-posedness of the coupled problem in the case of a linear Stokes problem. An iterative method to compute the solution is proposed. At each step this method requires the solution of one problem in the fluid part and one in the porous medium. Finally we introduce the Steklov-Poincare equation associated to the coupled problem.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7e5ef067103309608e098d9bf31d1b7c96b718b7

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Unified finite element discretizations of coupled Darcy–Stokes flow (2009, methodology): “Early numerical studies of the coupling of Darcy flow and Stokes flow can for example be found in [12, 22], while the more theoretical studies of such computations were initiated by the independent papers [15] and [16].”
Navier–Stokes/Forchheimer models for filtration through porous media (2013, background): “The three coupling conditions described in this section have been extensively 153 studied and analyzed also in [20, 21, 40, 45, 48, 51].”
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.”
Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition (2010, methodology): “Here, we will further exploit this parameter.”
A parallel domain decomposition method for coupling of surface and groundwater flows (2009, methodology): “The mathematical and numerical analysis of the model for the coupled problem has been well established in recent years [ 3 ,8,13,15,17].”
Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations (2004, methodology): “In a previous paper [ 5 ] we have introduced a differential system based on the coupling of (Navier) Stokes equations and Darcy equation for the modeling of the interaction between surface and subsurface flows.”
Coupling Fluid Flow with Porous Media Flow (2002, background): “[11] M. Discacciati, E. Miglio, and A. Quarteroni, Mathematical and numerical models for coupling surface and groundwater flows, Appl.”
Computational issues related to iterative coupling of subsurface and channel flows (2007, methodology): “The Neumann-Dirichlet algorithm [ 3 ,4] replaces the tightly coupled problems (13)–(15) by an iterative coupling process which converges to the solution of (13)–(15).”
A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow (2007, methodology): “For instance, the Beavers–Joseph–Saffman condition is used in [1, 21], while the free-slip condition with α = 0 is assumed in [10, 11, 12].”
Coupling Darcy and Stokes equations for porous media with cracks (2005, background): “Such interface conditions are studied for instance in [11,23] and ([9], Sect.”
A unified stabilized method for Stokes' and Darcy's equations (2007, unknown): “FINITE ELEMENT CENTER PREPRINT 2002–15”
Multirate time integration for coupled saturated/unsaturated porous medium and free flow systems (2015, methodology): “Mathematical models and numerical algorithms for solving such coupled flow problems have been developed and analyzed during the last decade mainly for stationary single-fluid-phase systems [11, 12, 26] that describe steady-state interactions between the free flow and saturated porous media.”