2016
DOI: 10.1137/15m101854x
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The Interface Control Domain Decomposition Method for Stokes--Darcy Coupling

Abstract: Abstract. The ICDD method [15,16] is here proposed to solve the coupling between Stokes and Darcy equations. According to this approach, the problem is formulated as an optimal control problem whose control variables are the traces of the velocity and the pressure on the internal boundaries of the subdomains that provide an overlapping decomposition of the original computational domain. A theoretical analysis is carried out and the well-posedness of the problem is proved under certain assumptions on both the g… Show more

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Cited by 19 publications
(22 citation statements)
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“…in the overlapping zone, we obtain the same result as in the monolithic case (29). In general, the last term of the second and forth equations vanishes when one has an overlap with more than one layer of elements.…”
Section: Dirichlet/dirichletsupporting
confidence: 75%
See 1 more Smart Citation
“…in the overlapping zone, we obtain the same result as in the monolithic case (29). In general, the last term of the second and forth equations vanishes when one has an overlap with more than one layer of elements.…”
Section: Dirichlet/dirichletsupporting
confidence: 75%
“…We point out that methods considering different types of transmission conditions on the interfaces of overlapping subdomains have been studied also in the context of the so-called virtual control methods [58,43], the least squares conjugate gradient method [44], and recently, the interface control domain decomposition methods [31,32,29]. …”
Section: Overlapping Subdomainsmentioning
confidence: 99%
“…In the robustness of ICDD versus the discretization parameters ( h and p ) as well as versus the overlap thickness δ=minboldx1@@Γ1,1emboldx2normalΓ2dist(boldx1,boldx2)>0 has been assessed.…”
Section: Numerical Results For the Stokes–darcy Couplingmentioning
confidence: 99%
“…In the second part of the paper, we consider the ICDD method to couple Stokes and Darcy equations. The method was formerly proposed and analyzed in . Here we further investigate it in some new applications, by considering nonhomogenous porous media, nonstraight interfaces, and ‘near normal flows’ (the less investigated cases in literature), and we compare it with the sharp interface approach based on the classical Beavers–Joseph–Saffman (BJS) conditions .…”
Section: Introductionmentioning
confidence: 99%
“…We note that ap¨,¨q and bp¨,¨q are equivalent to the bilinear forms presented in [44]; however, we introduce the additional term c Γ p¨,¨,¨q here as a means of enforcing the interface condition on Γ. While there are many means of imposing the interface conditions, such as the transition region approach proposed for Stokes-Darcy coupling in [20,21], we adopt here the form of c Γ given in (40) as it arises naturally from the stress, slip, and penetration conditions (32) when deriving the dG FE method.…”
Section: Discretization Of the Microscale Systemmentioning
confidence: 99%