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On bounded approximations of periodicity for computational homogenization of Stokes flow in porous media
Author(s) -
Sandström Carl,
Larsson Fredrik
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5281
Subject(s) - homogenization (climate) , bounded function , porous medium , mathematics , stokes flow , lagrange multiplier , periodic boundary conditions , mathematical analysis , stokes problem , flow (mathematics) , boundary value problem , representative elementary volume , finite element method , porosity , mathematical optimization , geometry , physics , materials science , thermodynamics , biodiversity , ecology , biology , composite material
Summary 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. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd