Mixed stabilized finite element method for the stationary Stokes-dual-permeability fluid flow model

Mahbub, Md. Abdullah Al; Shi, Feng; Nasu, Nasrin Jahan; Wang, Yongshuai; Zheng, Haibiao

doi:10.1016/j.cma.2019.112616

Cited by 25 publications

(9 citation statements)

References 65 publications

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“…Furthermore, they analyzed the well-posedness of the model and numerically solved in four different full discretization schemes. At present, the research on this model can be found in literatures [31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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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“…The authors used the dual-porosity equations over Darcy's region to describe fluid flowing through the multiple porous medium. Recently, several related research on the above model can be found in the literatures [2,3,24,29,44]. In particular, Gao and Li [24] proposed a decoupled stabilized finite element method to solve the coupled dual-porosity-Navier-Stokes fluid flow model in the numerical field.…”

Section: Introductionmentioning

confidence: 99%

On the solution of the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition

Yang,

He,

Cao

2020

Preprint

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In this work, we propose a new analysis strategy to establish an a priori estimate of the weak solutions to the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition. The most advantage of our proposed method is that the a priori estimate and the existence result are independent of small data and the large viscosity restriction. Therefore the global uniqueness of the weak solution is naturally obtained.

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“…In 2016, Hou et al proposed and numerically solved a coupled dual-porosity-Stokes multi-physics interface system [15] where dual-porosity equations were used to describe the multiple porous media flow. At present, the research on this model can be found in the literature [16,17,18,19]. To our best knowledge, up till now, there has been no research on the dual-porosity-Navier-Stokes model.…”

Section: Introductionmentioning

confidence: 99%

Decoupled Modified Characteristic Finite Element Method with Different Subdomain Time Steps for Nonstationary Dual-Porosity-Navier-Stokes Model

Cao¹,

Li³

2020

Preprint

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In this paper, we develop the numerical theory of decoupled modified characteristic finite element method with different subdomain time steps for the mixed stabilized formulation of nonstationary dual-porosity-Navier-Stokes model. Based on partitioned time-stepping methods, the system is decoupled, which means that the Navier-Stokes equations and two different Darcy equations are solved independently at each time step of subdomain. In particular, the Navier-Stokes equations are solved by the modified characteristic finite element method, which overcome the computational difficulties caused by the nonlinear term. In order to increase the efficiency, different time steps are used to different subdomains. The stability of this method is proved. In addition, we verify the optimal L 2 -norm error convergence order of the solutions by mathematical induction, whose proof implies the uniform L ∞ -boundedness of the fully discrete velocity solution. Finally, some numerical tests are presented to show efficiency of the proposed method.

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Mixed stabilized finite element method for the stationary Stokes-dual-permeability fluid flow model

Cited by 25 publications

References 65 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

On the solution of the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition

Decoupled Modified Characteristic Finite Element Method with Different Subdomain Time Steps for Nonstationary Dual-Porosity-Navier-Stokes Model

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