On bounded approximations of periodicity for computational homogenization of Stokes flow in porous media. (30th June 2016)

• Record Type: Journal Article
• Authors: Sandström, Carl; Larsson, Fredrik
• Is Part Of: International journal for numerical methods in engineering. Volume 109:Number 3(2017)
• Page Start: 307
• Page End: 325
• Publication Date: 2016-06-30
• Subjects: incompressible flow -- multiscale -- viscous flow -- finite element methods -- permeability -- bounds; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5281
• Languages: English
• ISSNs: 0029-5981

Abstract

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