Domain decomposition method for the fully-mixed Stokes–Darcy coupled problem

Sun, Yizhong; Sun, Weiwei; Zheng, Haibiao

doi:10.1016/j.cma.2020.113578

Cited by 25 publications

(30 citation statements)

References 40 publications

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“…In [9], the authors proved the BJ interface condition is more accurate compared with BJS interface condition from a mathematical point of view. There has been a great deal of achievements for solving such system [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The Robin-Robin domain decomposition methods, as a sense of continuous decoupling method, provides a natural and efficient means for multi-domain and multi-physics coupled problems.…”

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 flow is often modeled by the incompressible Stokes equations in the free domain and the Darcy equations in the porous domain, coupled across the interface through suitable conditions. The numerical solutions of these flows have been almost exclusively based on the finite element method [53,38,20,15,27,14,11,17,2,21,22,24,26,28,37,41,42]; a singularity method was used to obtain the solution in [23,48], and a MAC scheme in [52]. There are also recently developed partitioned methods for time-dependent Stokes-Biot problems, which utilize Robin-type coupling conditions at the interface [10,1].…”

Section: Introductionmentioning

confidence: 99%

“…For the coupled flow problem, similar techniques have been developed and investigated in the context of the finite element method, e.g. [53,12,57,47,21,22,24]. In particular, we are interested in the Dirichlet-Neumann iterative methods [47,21], where the interface conditions are split between the Stokes and Darcy problems.…”

Section: Introductionmentioning

confidence: 99%

A domain decomposition solution of the Stokes-Darcy system in 3D based on boundary integrals

Tlupova

2021

Preprint

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A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions and solving separate Stokes and Darcy problems iteratively. Second kind boundary integral equations are formulated for each problem. The integral equations use a smoothing of the kernels that achieves high accuracy on the boundary, and a straightforward quadrature to discretize the integrals. Numerical results demonstrate the convergence, accuracy, and dependence on parameter values of the iterative solution for a problem of viscous flow around a porous sphere with a known analytical solution, as well as more general surfaces.

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“…To reduce the computational costs, we aim to devise a domain decomposition method based on the proposed spatial discretization, where the global formulation is decomposed into the Stokes subproblem and the Darcy subproblem by using newly constructed Robin-type interface conditions. The construction of the novel Robin-type interface condition is not a simple extension of the method introduced in [30], instead it takes advantage of the special features of staggered DG method. Moreover, the compatibility conditions are derived to ensure the equivalence of the modified discrete formulation and the original discrete formulation.…”

Section: Introductionmentioning

confidence: 99%

A Robin-type domain decomposition method for a novel mixed-type DG method for the coupled Stokes-Darcy problem

Zhao¹

2021

Preprint

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In this paper, we first propose and analyze a novel mixed-type DG method for the coupled Stokes-Darcy problem on simplicial meshes. The proposed formulation is locally conservative. A mixed-type DG method in conjunction with the stress-velocity formulation is employed for the Stokes equations, where the symmetry of stress is strongly imposed. The staggered DG method is exploited to discretize the Darcy equations. As such, the discrete formulation can be easily adapted to account for the Beavers-Joseph-Saffman interface conditions without introducing additional variables. Importantly, the continuity of normal velocity is satisfied exactly at the discrete level. A rigorous convergence analysis is performed for all the variables. Then we devise and analyze a domain decomposition method via the use of Robin-type interface boundary conditions, which allows us to solve the Stokes subproblem and the Darcy subproblem sequentially with low computational costs. The convergence of the proposed iterative method is analyzed rigorously. In particular, the proposed iterative method also works for very small viscosity coefficient. Finally, several numerical experiments are carried out to demonstrate the capabilities and accuracy of the novel mixed-type scheme, and the convergence of the domain decomposition method.

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Domain decomposition method for the fully-mixed Stokes–Darcy coupled problem

Cited by 25 publications

References 40 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

A domain decomposition solution of the Stokes-Darcy system in 3D based on boundary integrals

A Robin-type domain decomposition method for a novel mixed-type DG method for the coupled Stokes-Darcy problem

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