A second‐order partitioned method with different subdomain time steps for the evolutionary Stokes‐Darcy system

Yi, Li; Hou, Yanren

doi:10.1002/mma.4744

Cited by 32 publications

(13 citation statements)

References 30 publications

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“…At present, researchers pay more and more attention to the unsteady model and adopt different methods to obtain time semi-discrete results. Such as the partitioned methods [24,25,26,27], the monolithic discretization methods [28,29,30]. All the methods mentioned in the paper are related to theoretical analysis and numerical experiments.…”

Section: Introductionmentioning

confidence: 99%

Analysis of A New Time Filter Algorithm for The Unsteady Stokes/Darcy Model

Qu¹,

Wang²,

Li³

et al. 2022

Preprint

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This paper first presents a first order θ−scheme which is one parameter family of Linear Multistep Methods for the unsteady Stokes/Darcy model. Then, on the basis of this scheme, we use a time filter algorithm to increase the convergence order to the second order with almost no increasing the amount of computation, from which we get a new efficient algorithm. Finally, we theoretically analyze the stabilities and error estimations of coupled and decoupled schemes respectively, and we also do some numerical experiments to verify the effectiveness, convergence and efficiency.

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Section: Introductionmentioning

confidence: 99%

Analysis of A New Time Filter Algorithm for The Unsteady Stokes/Darcy Model

Qu¹,

Wang²,

Li³

et al. 2022

Preprint

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show abstract

“…Therefore, it is reasonable to apply different time steps in different subdomains. For coupled free flow and porous media flow with different subdomain time steps, see [20,21,22,23,24] and the references therein. And for the difficulties, it is a coupling problem.…”

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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“…Shan et al [36] have analyzed a multirate and decoupling algorithm for the coupled time-dependent Stokes equations with Darcy's law, which allows different time steps in the fluid region and the porous region. Later, as an extension of the decoupling algorithm for the Stokes-Darcy system, the second-order backward differentiation formula [20], the second-order spectral deferred correction method [41], and an explicit leap frog method [19] have been designed. Besides that, the differing time steps method has been extended to the Navier-Stokes/Darcy model [14], the Darcy-Brinkman problem [22], and to the nematic liquid crystal flow [21].…”

mentioning

confidence: 99%

A decoupling finite element method with different time steps for the micropolar fluid model

Huang¹,

Liao²

2022

etna

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In this paper, a decoupling finite element method with different time steps for the micropolar fluid model is considered. The theoretical analysis shows that the proposed method is stable and convergent. Further, in order to show the efficiency of the method, we present some numerical results for a problem with analytical solution, and we test the method for the stirring problem of a passive scalar. From these numerical results, we can see that the method is efficient for micropolar fluid flows.

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A second‐order partitioned method with different subdomain time steps for the evolutionary Stokes‐Darcy system

Cited by 32 publications

References 30 publications

Analysis of A New Time Filter Algorithm for The Unsteady Stokes/Darcy Model

Analysis of A New Time Filter Algorithm for The Unsteady Stokes/Darcy Model

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

A decoupling finite element method with different time steps for the micropolar fluid model

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