Homogenization of the Stokes equation with mixed boundary condition in a porous medium

Fabricius, John; Miroshnikova, Elena; Wall, Peter

doi:10.1080/23311835.2017.1327502

Cited by 8 publications

(1 citation statement)

References 21 publications

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“…Finally, [12,30] proved that the microscale pressure in the porous medium strongly converges to the macroscopic Darcy pressure like √ ℓ with respect to the L 2 norm in Ω p when a boundary condition on the Cauchy stress is imposed on the top boundary of the periodic microscale porous medium. This boundary condition converges to a macroscale Dirichlet boundary condition for the pressure (see, e.g., [12,25]) analogous to the one that we impose on Γ p , and we numerically observe the correct convergence rate for the ICDD Darcy pressure. The order of convergence of the L 2 norm of the error of the fluid velocity also agrees with the theoretical estimate in [12].…”

Section: Error Convergence Ratesmentioning

confidence: 55%

The Interface Control Domain Decomposition Method for Stokes--Darcy Coupling

Discacciati¹,

Gervasio²,

Giacomini³

et al. 2016

SIAM J. Numer. Anal.

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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 geometry and the model parameters. An efficient solution algorithm is proposed, and several numerical tests are implemented. Our results show the accuracy of the ICDD method, its computational efficiency and robustness with respect to the different parameters involved (grid-size, polynomial degrees, permeability of the porous domain, thickness of the overlapping region). The ICDD approach turns out to be more versatile and easier to implement than the celebrated model based on the Beavers, Joseph and Saffman coupling conditions.

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Section: Error Convergence Ratesmentioning

confidence: 55%

The Interface Control Domain Decomposition Method for Stokes--Darcy Coupling

Discacciati¹,

Gervasio²,

Giacomini³

et al. 2016

SIAM J. Numer. Anal.

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Pressure-driven flow in a thin pipe with rough boundary

Miroshnikova

2020

Z. Angew. Math. Phys.

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Stationary incompressible Newtonian fluid flow governed by external force and external pressure is considered in a thin rough pipe. The transversal size of the pipe is assumed to be of the order $$\varepsilon $$ ε , i.e., cross-sectional area is about $$\varepsilon ^{2}$$ ε 2 , and the wavelength in longitudinal direction is modeled by a small parameter $$\mu $$ μ . Under general assumption $$\varepsilon ,\mu \rightarrow 0$$ ε , μ → 0 , the Poiseuille law is obtained. Depending on $$\varepsilon ,\mu $$ ε , μ -relation ($$\varepsilon \ll \mu $$ ε ≪ μ , $$\varepsilon /\mu \sim \mathrm {constant}$$ ε / μ ∼ constant , $$\varepsilon \gg \mu $$ ε ≫ μ ), different cell problems describing the local behavior of the fluid are deduced and analyzed. Error estimates are presented.

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