On bounded approximations of periodicity for computational homogenization of Stokes flow in porous media
Journal article, 2017

By separation of scales and the homogenization of a flow through porous media, a two-scale problem arises where a Darcy-type flow is present on the macroscale and a Stokes flow on the subscale. In this paper, the problem is given as the minimization of a potential. Additional constraints imposing periodicity in a weak sense are added using Lagrange multipliers. In particular, the upper and lower energy bounds for the corresponding strongly periodic problem are produced, quantifying the accuracy of the weakly periodic boundary conditions. A numerical example demonstrates the evaluation of energy bounds and the performance of weakly periodic boundary conditions on a representative volume element.

bounds

Engineering

formulation

viscous flow

incompressible flow

multiscale

finite element methods

permeability

permeability

Mathematics

Author

Carl Sandström

Chalmers, Applied Mechanics, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

International Journal for Numerical Methods in Engineering

0029-5981 (ISSN) 1097-0207 (eISSN)

Vol. 109 3 307-325

Subject Categories

Materials Engineering

Areas of Advance

Materials Science

DOI

10.1002/nme.5281

More information

Created

10/7/2017