Partitioned Time Stepping Method for Fully Evolutionary Stokes--Darcy Flow with Beavers--Joseph Interface Conditions

Shan, Li; Zheng, Haibiao

doi:10.1137/110828095

Cited by 106 publications

(38 citation statements)

References 19 publications

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“…But, the disadvantage of the two schemes is one has to solve a large coupled algebraic system at each time level, which is very time consuming in numerical computation. The decoupled or partition methods are very efficient to solve multi-physics problems, such as Stokes-Darcy problems [25][26][27][28][29][30], fluid-fluid problems [31] and Stokes-Biot problems [32]. Inspired by the existing works, we proposed a decoupled time discretization scheme for MHD equations in [33] to cope with the drawback of the semi-implicit and implicit schemes.…”

Section: Introductionmentioning

confidence: 99%

Decoupled schemes for unsteady MHD equations II: Finite element spatial discretization and numerical implementation

Zhang

2015

Computers & Mathematics with Applications

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a b s t r a c tIn this article, a decoupled fully discrete scheme for solving 2D magnetohydrodynamics (MHD) equations is proposed. The decoupled scheme is used for time discretization, and the finite element method is used for spatial discretization. Firstly, the almost unconditional stability ( t ≤ C ) of this scheme is established. Then optimal L 2 and H 1 error estimates of numerical solution are provided. Finally, a numerical example is presented to confirm our theoretical results and show the high efficiency of the decoupled scheme.

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Section: Introductionmentioning

confidence: 99%

Decoupled schemes for unsteady MHD equations II: Finite element spatial discretization and numerical implementation

Zhang

2015

Computers & Mathematics with Applications

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“…For the analysis and numerical methods for Stokes-Darcy systems with Beavers-Joseph condition, we refer to [21,26,40].…”

Section: Interface Conditionsmentioning

confidence: 99%

Non-Iterative Partitioned Methods for Uncoupling Evolutionary Groundwater–Surface Water Flows

Kubacki

Tran

2017

Fluids

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Abstract:We present an overview of a modern, efficient approach for uncoupling groundwater-surface water flows governed by the fully evolutionary Stokes-Darcy equations. Referred to as non-iterative partitioned methods, these algorithms treat the coupling terms explicitly and at each time level require only one Stokes and one Darcy sub-physics solve, thus taking advantage of existing solvers optimized for each sub-flow. This strategy often results in a time-step condition for stability. Furthermore, small problem parameters, specifically those related to the physical characteristics of the porous media domain, can render certain time-step conditions impractical. Despite these obstacles, researchers have made significant progress towards efficient, stable, and accurate partitioned methods. Herein, we provide a comprehensive survey and comparison of recent developments utilizing these non-iterative numerical schemes.

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“…To examine the orders of convergence with respect to the time step ∆t, we introduce a more accurate, but slightly more sophisticated approach [30].…”

Section: Elliptic-elliptic Ds Equations Example 1 Defocusing Ds Equamentioning

confidence: 99%

A time-splitting Galerkin finite element method for the Davey–Stewartson equations

Gao

Mei

2015

Computer Physics Communications

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Partitioned Time Stepping Method for Fully Evolutionary Stokes--Darcy Flow with Beavers--Joseph Interface Conditions

Cited by 106 publications

References 19 publications

Decoupled schemes for unsteady MHD equations II: Finite element spatial discretization and numerical implementation

Decoupled schemes for unsteady MHD equations II: Finite element spatial discretization and numerical implementation

Non-Iterative Partitioned Methods for Uncoupling Evolutionary Groundwater–Surface Water Flows

A time-splitting Galerkin finite element method for the Davey–Stewartson equations

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