Weakly periodic boundary conditions for the homogenization of flow in porous media
Journal article, 2014

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.

Porous media

Computational homogenization

Multiscale modeling

Weak periodicity

Stokes flow

Author

Carl Sandström

Chalmers, Applied Mechanics, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Kenneth Runesson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Advanced Modeling and Simulation in Engineering Sciences

2213-7467 (eISSN)

Vol. 1

Subject Categories

Mechanical Engineering

Areas of Advance

Materials Science

DOI

10.1186/s40323-014-0012-6

More information

Latest update

8/10/2023