Least squares approach for the time-dependent nonlinear Stokes–Darcy flow

Lee, Hyesuk; Rife, Kelsey

doi:10.1016/j.camwa.2014.04.002

Cited by 11 publications

(3 citation statements)

References 19 publications

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“…These methods are non-iterative by using an explicit method for the coupling terms, and the key issue is how to achieve desired accuracy and stability properties. A different approach was proposed in [48] by formulating the coupled problem as a constrained optimal control problem which is solved at each time step by a least square method (thus, the same time step is used in both regions).…”

Section: Introductionmentioning

confidence: 99%

“…The difference between these two types of fluid lies in the viscosity which is a constant for Newtonian fluids and a function of the magnitude of the deformation tensor for non-Newtonian fluids (more discussion can be found in [31]). Mathematically, one deals with a linear or nonlinear coupled flow problem; the nonlinear Stokes-Darcy coupling was considered in [31,32,48,30]. In addition, approximation methods for the nonlinear Navier-Stokes/Darcy system were studied in [29,39,10,21,22,18], and for the coupling with transport in [62,17,56].…”

Section: Introductionmentioning

confidence: 99%

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A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows

Hoang¹,

Lee²

2020

Preprint

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We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on the interface condition for mass conservation. The nonlinear interface problem is then solved by a nested iteration approach which involves, at each Newton iteration, the solution of a linearized interface problem and, at each Krylov iteration, parallel solution of time-dependent linearized Stokes and Darcy problems. Consequently, local discretizations in time (and in space) can be used to efficiently handle multiphysics systems of coupled equations evolving at different temporal scales. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows

Hoang¹,

Lee²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Over the last few decades, a great deal of effort has been devoted to developing an appropriate approximate solution to study the Stokes-Darcy model. Many different techniques and numerical methods were applied to investigate the Stokes-Darcy fluid flow model, such as coupled finite elements methods [15][16][17][18][19][20][21], two-grid/multi-grid methods [22][23][24][25][26][27][28], discontinuous Galerkin finite element methods [29][30][31][32], partitioned time stepping methods [33][34][35][36], least squares methods [37][38][39], domain decomposition methods [1,2,4,[40][41][42][43][44][45][46][47][48], local-parallel finite element methods [49], interface relaxation method [50,51], motar finite element methods [52,53], Lagrange multiplier methods [11,[54][55]…”

Section: Introductionmentioning

confidence: 99%

Stabilized finite element method for the stationary mixed Stokes–Darcy problem

Mahbub

Shi

et al. 2018

Adv Differ Equ

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This paper considers numerical methods for solving the viscous incompressible steady-state Stokes-Darcy problem that can be implemented by the use of existing surface water and groundwater codes. In the porous medium problem for subsurface flow, a mixed discretization, which describes the macroscopic properties of a filtration process and is vigorous with respect to the variations in the material data, is often advocated. However, the theory of mixed spacial discretizations to Stokes-Darcy problems is far less developed than non-mixed versions. We develop herein a new robust stabilized fully mixed discretization technique in the porous media region coupled with the fluid region via the physically appropriate coupling conditions on the interface. The method developed here does not use any Lagrange multiplier and introduces a stabilization term in the temporal discretization to ensure the stability of the finite element scheme. The well-posedness of the finite element scheme and its convergence analysis are also derived. Finally, the efficiency and accuracy of the numerical methods are illustrated by several testing examples.

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A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition

Liu

Chen

2019

Calcolo

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Least squares approach for the time-dependent nonlinear Stokes–Darcy flow

Cited by 11 publications

References 19 publications

A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows

A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows

Stabilized finite element method for the stationary mixed Stokes–Darcy problem

A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition

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