A linear, decoupled fractional time‐stepping method for the nonlinear fluid–fluid interaction

Li, Jian; Huang, Pengzhan; Zhang, Chong; Guo, Ge

doi:10.1002/num.22382

Cited by 17 publications

(6 citation statements)

References 39 publications

(59 reference statements)

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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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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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“…Theorem 2 (Unconditional stability of MBELF scheme) Let u n+1 ∈ X h satisfy (12) for n = 1, 2, … , N − 1, there exist a constant C independent of Δt and h, such that…”

Section: Stabilities Of Numerical Algorithmsmentioning

confidence: 99%

“…Besides, Qian et al studied a fully discrete Crank–Nicolson leap‐frog (CNLF) time stepping decoupled scheme for atmosphere–ocean coupling system [11], the nonlinear interface term still decoupled by using GA strategy for the interface jump term. In the meantime, Li et al proposed a linear decoupled fractional time stepping method [12], for each fluid, the velocity, and pressure were respectively determined by just solving one vector‐valued quasi‐elliptic equation and the Poisson equation with homogeneous Neumann boundary condition per time step. They also proposed a parallel non‐spatial iterative and rotational pressure projection method in Reference [13].…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of two decoupled algorithms for a parabolic two domain problem

Shan

Zhang

2022

Numerical Methods Partial

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To investigate the fluid-fluid interaction problem, we study two first-order in time, decoupled algorithms for a coupling system. This system consist of two heat equations, which are coupled by a condition that allows energy to pass back and forth across the interface. The first scheme is a combination of the three-level implicit method with the coupling terms treated by the explicit leap-frog method. Under a time step size condition, we prove that it is stable and first-order convergent. To remove the time step size condition, we modify the treatment of the coupling interface term and propose a second scheme. Instead of making the interface term explicitly, we only lag the variable in the different subdomain onto the previous time step. As expected, the second scheme is proved to be stable and convergent unconditionally. Since both schemes only require the solution of two decoupled heat equations at each time step. Hence, they are efficient in computation and can be easily implemented by using legacy codes. The numerical tests also confirm our theoretical results. KEYWORDSa parabolic two domain problem, atmosphere-ocean interaction, partitioned time stepping method

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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%

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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A linear, decoupled fractional time‐stepping method for the nonlinear fluid–fluid interaction

Cited by 17 publications

References 39 publications

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

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

Numerical analysis of two decoupled algorithms for a parabolic two domain problem

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

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