Coupling of Darcy–Forchheimer and Compressible Navier–Stokes Equations with Heat Transfer

Amara, Mohamed; Capatina, Daniela; Lizaik, Layal

doi:10.1137/070709517

Cited by 24 publications

(17 citation statements)

References 12 publications

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“…In recent years, many scientists and engineers have investigated the fluid flow interaction between the conduit and porous media regime . The massive applications, such as karst aquifer subsurface flow system, interaction between the surface flows and subsurface flows, petroleum extraction, industrial filtration, biochemical transport, field flow fractionation for separation and characterization of proteins, blood flow in arteries and veins, etc, attract scientists and engineers to build related fluid dynamical models, including (Navier‐)Stokes‐Darcy model, Stokes‐Darcy‐transport model, Darcy‐Stokes‐Brinkman model, etc . It is not surprising that a great deal of effort has been devoted to develop appropriate numerical methods to solve the (Navier‐)Stokes‐Darcy fluid flow system, including coupled finite element methods, domain decomposition methods, Lagrange multiplier methods, mortar finite element methods, least‐square methods, partitioned time‐stepping methods, two‐grid and multigrid methods, discontinuous Galerkin finite element methods, boundary integral methods, and many others …”

Section: Introductionmentioning

confidence: 99%

Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Mahbub

Nasu

et al. 2019

Numerical Meth Engineering

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In this paper, we propose and analyze two stabilized mixed finite element methods for the dual-porosity-Stokes model, which couples the free flow region and microfracture-matrix system through four interface conditions on an interface. The first stabilized mixed finite element method is a coupled method in the traditional format. Based on the idea of partitioned time stepping, the four interface conditions, and the mass exchange terms in the dual-porosity model, the second stabilized mixed finite element method is decoupled in two levels and allows a noniterative splitting of the coupled problem into three subproblems. Due to their superior conservation properties and convenience of the computation of flux, mixed finite element methods have been widely developed for different types of subsurface flow problems in porous media. For the mixed finite element methods developed in this article, no Lagrange multiplier is used, but an interface stabilization term with a penalty parameter is added in the temporal discretization. This stabilization term ensures the numerical stability of both the coupled and decoupled schemes. The stability and the convergence analysis are carried out for both the coupled and decoupled schemes. Three numerical experiments are provided to demonstrate the accuracy, efficiency, and applicability of the proposed methods. KEYWORDS decoupled numerical methods, dual-porosity-Stokes model, horizontal wellbore, mixed finite elements, stabilization Int J Numer Methods Eng. 2019;120:803-833. wileyonlinelibrary.com/journal/nme 804 AL MAHBUB ET AL.model, It is not surprising that a great deal of effort has been devoted to develop appropriate numerical methods to solve the (Navier-)Stokes-Darcy fluid flow system, including coupled finite element methods, 17-21 domain decomposition methods, 22-31 Lagrange multiplier methods, 3,32,33 mortar finite element methods, 34,35 least-square methods, 36-38 partitioned time-stepping methods, 39,40 two-grid and multigrid methods, 41-44 discontinuous Galerkin finite element methods, 45-50 boundary integral methods, 51,52 and many others. [53][54][55][56][57][58] Although the traditional Stokes-Darcy model has been well studied, it has limitation to describe the heterogeneity of the porous medium which contains multiple porosities. It is worth to notice that the realistic naturally fractured reservoir consists of two coexisting and interacting medium, namely, tight matrix and microfractures. Furthermore, it is more important to characterize the intrinsic properties and accurately modeled the flow interactions between each medium. 59,60 The first multiporosity model was proposed by Barenblatt et al 61 for the naturally fractured reservoir in 1960 where the microfracture and matrix systems are formulated by individual but overlapping continua. Warren and Root 62 developed a homogeneous orthotropic dual-porosity model in 1963 based on the model proposed by Barenblatt. There are many applications for the dual-porosity model such as the geothermal system, hydrogeology, pe...

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Section: Introductionmentioning

confidence: 99%

Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Mahbub

Nasu

et al. 2019

Numerical Meth Engineering

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“…Many other methods have been developed to solve the Darcy-Stokes(-Brinkman) and other similar models; see [3,8,[10][11][12]16,15,27,42,52,53,55,56,62,63,66,68,69] and the reference cited therein. Among these methods, the domain decomposition method [1,14,39,51,57,67], which can be traced back to [2], is more natural than others because the problem domain naturally consists of two different subdomains and because parallel computation is facilitated; see, e.g., [25] for the BJS condition and [28][29][30][31][32][33]43,46] for simplified BJS conditions.…”

Section: Introductionmentioning

confidence: 99%

Robin–Robin domain decomposition methods for the steady-state Stokes–Darcy system with the Beavers–Joseph interface condition

et al. 2011

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Domain decomposition methods for solving the coupled Stokes-Darcy system with the Beavers-Joseph interface condition are proposed and analyzed. Robin boundary conditions are used to decouple the Stokes and Darcy parts of the system. Then, parallel and serial domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence of the two methods is demonstrated and the results of computational experiments are presented to illustrate the convergence.Mathematics Subject Classification (2010) 65M55 · 65M12 · 65M15 · 65M60 · 35M10 · 35Q35 · 76D07 · 76S05

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“…Many other methods have been developed to solve the Stokes-Brinkman and other similar models; see [1,3,[5][6][7]28,30,34,36,37] and the reference cited therein. Among these methods, domain decomposition is more natural than others because the problem domain naturally consists of two different subdomains and because parallel computation is facilitated; see, e.g., [12] for the BJSJ condition and [13][14][15][16][17][18]23] for simplified BJSJ conditions.…”

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confidence: 99%

A Parallel Robin–Robin Domain Decomposition Method for the Stokes–Darcy System

Chen¹,

Gunzburger²,

Hua³

et al. 2011

SIAM J. Numer. Anal.

145

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Coupling of Darcy–Forchheimer and Compressible Navier–Stokes Equations with Heat Transfer

Cited by 24 publications

References 12 publications

Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

Robin–Robin domain decomposition methods for the steady-state Stokes–Darcy system with the Beavers–Joseph interface condition

A Parallel Robin–Robin Domain Decomposition Method for the Stokes–Darcy System

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