Numerical modelling of coupled surface and subsurface flow systems

Chidyagwai, Prince; Rivière, Béatrice

doi:10.1016/j.advwatres.2009.10.012

Cited by 32 publications

(21 citation statements)

References 21 publications

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“…When the meshes align at the interface, direct transfer can be used effectively. For an illustration, consider coupling Navier-Stokes flow on the surface and Darcy flow in subsurface porous media (Figure 12) (Chidyagwai and Rivière, 2010). The free-flow region is denoted Ω 1 , and the porous medium is represented as several layers (regions A, B, C) with different permeability and faults (region D).…”

Section: Methods For Coupling Multiphysics Components In Spacementioning

confidence: 99%

Multiphysics simulations: challenges and opportunities.

Keyes¹,

McInnes²,

Woodward³

et al. 2012

149

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We consider multiphysics applications from algorithmic and architectural perspectives, where "algorithmic" includes both mathematical analysis and computational complexity and "architectural" includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

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Section: Methods For Coupling Multiphysics Components In Spacementioning

confidence: 99%

Multiphysics simulations: challenges and opportunities.

Keyes¹,

McInnes²,

Woodward³

et al. 2012

149

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show abstract

“…In this context, preconditioned GMRES methods with block or constraint preconditioners [10,15,16] usually show a mesh-independent convergence Downloaded 12/19/17 to 131.211.208. 19.…”

Section: Multiblock Multigrid Algorithmmentioning

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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“…The steadystate case has been mostly studied by Discacciati in [14], by Discacciati and Quarteroni in [15,16], by Badea et al in [5], by Girault and Rivière in [18], and by Chidyagwai and Rivière in [11,12]. To our knowledge, the time-dependent coupled Navier-Stokes/Darcy problem, with Beavers-Joseph-Saffmann interface condition, has only been mathematically and numerically analyzed by Ç eşmelioglu and Rivière in [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…The surface region of Ω is denoted by Ω 1 and the subsurface region is denoted by Ω 2 with Lipschitz continuous boundaries ∂Ω 1 and ∂Ω 2 . The interface separating the surface and the subsurface regions is denoted by 12 , i = 1, 2 corresponding to the outer boundaries of the surface and subsurface. Finally, the boundary Γ 2 is decomposed into two disjoint open sets:…”

Section: Statement Of the Problemmentioning

confidence: 99%