A Two-Grid Method of a Mixed Stokes–Darcy Model for Coupling Fluid Flow with Porous Media Flow

Mu, Mo; Xu, Jinchao

doi:10.1137/050637820

Cited by 260 publications

(138 citation statements)

References 36 publications

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“…There has been considerable work done on efficient numerical solution algorithms for the Stokes-Laplace formulation. We refer the reader to [4,19,24] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Many of the applications considered use a Newtonian fluid in both the Stokes and Darcy regions, where the motivating problem is often a coupled surface water / groundwater model (see, for instance, [6,14,18,22,24,27,28]). Our interest in coupled flows arises from filtration applications, which continues to be an active area of research (see, for instance, [3,12,20,26,23]).…”

Section: Introductionmentioning

confidence: 99%

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Coupling nonlinear Stokes and Darcy flow using mortar finite elements

Ervin

Jenkins

Sun

2011

Applied Numerical Mathematics

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We study a system composed of a non-linear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions.

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“…There has been considerable work done on efficient numerical solution algorithms for the Stokes-Laplace formulation. We refer the reader to [4,19,24] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

Ervin

Jenkins

Sun

2011

Applied Numerical Mathematics

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“…In other works, decoupling strategies have been used for the solution of Stokes-Darcy problems, such as: iterative subdomain methods [8], Lagrange multipliers [31], two-grid method [37], among others. For instance, Mu and Zhu [36], who used the Saffman matching condition for the tangential velocities (which comes from disregarding the tangential Darcy velocity in the Beavers-Joseph condition), proposed and assessed a decoupling FEM methodology based on interface approximations via temporal extrapolation for non stationary cases.…”

Section: Description Of the Stokes-darcy Approachmentioning

confidence: 99%

Stokes–Brinkman formulation for prediction of void formation in dual-scale fibrous reinforcements: a BEM/DR-BEM simulation

et al. 2017

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A numerical study of voids formation in dualscale fibrous reinforcements is presented. Flow fields in channels (Stokes) and tows (Brinkman) capillary ratio, jump stress coefficient and two formulations (Stokes-Brinkman and Stokes-Darcy) on the filling process, void formation and void characterization. Filling times, fluid front shapes, void size and shape, time and space evolution of the saturation, are influenced by these parameters, but voids location is not.

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“…There are many appealing reasons as discussed in [18] that have led to active research on developing effective and efficient decoupling techniques for multi-physics mixed models so that existing single-model solvers can be applied locally with little extra computational and software overhead. Most of the decoupled methods for the Stokes-Darcy model in the literature are developed for the stationary case.…”

Section: Schemes For a Non-stationary Mixed Stokes-darcy Model 711mentioning

confidence: 99%

Decoupled schemes for a non-stationary mixed Stokes-Darcy model

Zhu

2009

Math. Comp.

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171

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Abstract. We study numerical methods for solving a non-stationary mixed Stokes-Darcy problem that models coupled fluid flow and porous media flow. A decoupling approach based on interface approximation via temporal extrapolation is proposed for devising decoupled marching algorithms for the mixed model. Error estimates are derived and numerical experiments are conducted to demonstrate the computational effectiveness of the decoupling approach.

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A Two-Grid Method of a Mixed Stokes–Darcy Model for Coupling Fluid Flow with Porous Media Flow

Cited by 260 publications

References 36 publications

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

Stokes–Brinkman formulation for prediction of void formation in dual-scale fibrous reinforcements: a BEM/DR-BEM simulation

Decoupled schemes for a non-stationary mixed Stokes-Darcy model

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