The efficient rotational pressure-correction schemes for the coupling Stokes/Darcy problem

Li, Jian; Yao, Meng; Mahbub, Md. Abdullah Al; Zheng, Haibiao

doi:10.1016/j.camwa.2019.06.033

Cited by 17 publications

(4 citation statements)

References 53 publications

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“…3, 4, 5 and 6, the fluid in the matrix domain does not directly communicate with the wellbore. From the streamlines in these pictures, the fluid is flowing from the matrix to the microfractures nearby, and then from microfractures to the vertical production wellbore, which is consistent with the literatures [31,33,36,53]. Left: the pressure in the microfractures and conduits; Right: the pressure in the matrix this method is a combination of domain decomposition method and the modified characteristic finite element method, which derives a decoupled and fully discrete parallel scheme without nonlinear term.…”

Section: Examplesupporting

confidence: 83%

A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition

Cao

2021

J Sci Comput

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In this paper, we propose and analyze the parallel Robin-Robin domain decomposition method based on the modified characteristic finite element method for the time-dependent dual-porosity-Navier-Stokes model with the Beavers-Joseph interface condition. For the coupling terms, we treat them in an explicit manner which takes advantage of information obtained in previous time steps to construct a non-iteration domain decomposition method. By this means, two single dual-porosity equations and a single Navier-Stokes equation are needed to solve at each time. In particular, we solve the Navier-Stokes equation by the modified characteristic finite element method, which avoids the computational inefficiency caused by the nonlinear convection term. Furthermore, we prove the error convergence of solutions by mathematical induction, whose proof implies the uniform L ∞ -boundedness of the fully discrete velocity solution in conduit flow. Finally, some numerical examples are presented to show the effectiveness and efficiency of the proposed method. KeywordsTime-dependent dual-porosity-Navier-Stokes model • Beavers-Joseph interface condition • Domain decomposition methods • Modified characteristic finite element methods • Parallel algorithms

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Section: Examplesupporting

confidence: 83%

A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition

Cao

2021

J Sci Comput

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“…Moreover, we achieve a series of numerical results for the presented problem [21][22][23]. Furthermore, we will then use the efficient methods [18,34,35,37] to solve the similar practical problem for the coupling problem.…”

Section: Resultsmentioning

confidence: 99%

A priori and a posteriori estimates of the stabilized finite element methods for the incompressible flow with slip boundary conditions arising in arteriosclerosis

Zheng

Zou

2019

Adv Differ Equ

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In this paper, we develop the lower order stabilized finite element methods for the incompressible flow with the slip boundary conditions of friction type whose weak solution satisfies a variational inequality. The H 1 -norm for the velocity and the L 2 -norm for the pressure decrease with optimal convergence order. The reliable and efficient a posteriori error estimates are also derived. Finally, numerical experiments are presented to validate the theoretical results. MSC: 35L70; 65N30; 76D06

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“…Then, the weak formulation of the dual-porosity-Navier-Stokes model (2.1)-(2.12) as follows [31][32][33][34][35][36]. we suppose ⃗ f s ∈ H −1 (Ω s ) and f d ∈ L 2 (Ω d ).…”

Section: Preliminaries Weak Formulations and Finite Element Spacesmentioning

confidence: 99%

“…Trace inequality: There exists a positive constant C T depending on the domain Ω s such that for all

{\overset{v}{true}}_{s} \in Y_{s}

, we have

‖ {\overset{v}{true}}_{s} ‖_{L^{2} false(double-struckI false)} \leq C_{T} ‖ {\overset{v}{true}}_{s} ‖_{0}^{\frac{1}{2}} ‖ \nabla v_{s} ‖_{0}^{\frac{1}{2}} .

Then, the weak formulation of the dual‐porosity‐Navier–Stokes model (2.1)–(2.12) as follows [31–36]. we suppose

{\overset{f}{true}}_{s} \in H^{- 1} false(Ω_{s} false)

and f d ∈ L 2 (Ω d ).…”

Section: Preliminaries Weak Formulations and Finite Element Spacesmentioning

confidence: 99%

A decoupled stabilized finite element method for the dual‐porosity‐Navier–Stokes fluid flow model arising in shale oil

Gao

2020

Numerical Methods Partial

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In this paper, we consider the decoupled stabilized finite element method for the dual-porosity-Navier-Stokes model coupling the free flow region and the microfracture-matrix system by using four interface conditions on the interface. The stabilized finite element method is decoupled in two levels, and it allows the coupling problem to be divide into three subproblems in a non-iterative manner, which improves the computational efficiency. In addition, the stability and convergence of the decoupling scheme are also analyzed. Finally, the theoretical results are illustrated by some numerical experiments. KEYWORDS convergence, decoupled method, dual-porosity-Navier-Stokes, finite element method, numerical experiments, stability 1 INTRODUCTION Many scientists and engineers have investigated the fluid flow interaction between conduit and porous media region [1-3]. A large number of practical problems, such as groundwater flow system, interaction between surface, and groundwater flow, biochemical transportation, blood flow in artery, vein, and so forth [4-7], have been established relevant hydrodynamic models by scientists. In addition, a lot of efforts have been devoted to develop appropriate numerical methods to solve the Stokes-Darcy fluid system, including the coupled finite element methods [8-10], domain decomposition methods [11-13], the Lagrange multiplier method [14, 15], and so forth. Although the traditional Stokes-Darcy model [16-18] has been well studied, it has some limitations in describing the heterogeneity of porous media. It is worth noting that the real natural fractured

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The efficient rotational pressure-correction schemes for the coupling Stokes/Darcy problem

Cited by 17 publications

References 53 publications

A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition

A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition

A priori and a posteriori estimates of the stabilized finite element methods for the incompressible flow with slip boundary conditions arising in arteriosclerosis

A decoupled stabilized finite element method for the dual‐porosity‐Navier–Stokes fluid flow model arising in shale oil

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