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Weakly periodic boundary conditions for the homogenization of flow in porous media

Carl Sandström (Institutionen för tillämpad mekanik, Material- och beräkningsmekanik) ; Fredrik Larsson (Institutionen för tillämpad mekanik, Material- och beräkningsmekanik) ; Kenneth Runesson (Institutionen för tillämpad mekanik, Material- och beräkningsmekanik)
Advanced Modeling and Simulation in Engineering Sciences (2213-7467). Vol. 1 (2014),
[Artikel, refereegranskad vetenskaplig]

Background
Seepage in porous media is modeled as a Stokes flow in an open pore system contained in a rigid, impermeable and spatially periodic matrix. By homogenization, the problem is turned into a two-scale problem consisting of a Darcy type problem on the macroscale and a Stokes flow on the subscale.

Methods
The pertinent equations are derived by minimization of a potential and in order to satisfy the Variationally Consistent Macrohomogeneity Condition, Lagrange multipliers are used to impose periodicity on the subscale RVE. Special attention is given to the bounds produced by confining the solutions spaces of the subscale problem.

Results
In the numerical section, we choose to discretize the Lagrange multipliers as global polynomials along the boundary of the computational domain and investigate how the order of the polynomial influence the permeability of the RVE. Furthermore, we investigate how the size of the RVE affect its permeability for two types of domains.

Conclusions
The permeability of the RVE depends highly on the discretization of the Lagrange multipliers. However, the flow quickly converges towards strong periodicity as the multipliers are refined.

Nyckelord: Multiscale modeling, Computational homogenization, Stokes flow, Weak periodicity, Porous media



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Denna post skapades 2015-01-19. Senast ändrad 2015-06-18.
CPL Pubid: 211068

 

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Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Material- och beräkningsmekanik (2005-2017)

Ämnesområden

Materialvetenskap
Maskinteknik

Chalmers infrastruktur

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