Multiscale modeling and simulation of fluid flows in highly deformable porous media

P. Popov*, Y. Efendiev, Y. Gorb

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

In this work a new class of methods for upscaling Fluid-Structure Interaction (FSI) problems from the pore-level to a macroscale is proposed. A fully coupled FSI problem for Stokes fluid and an elastic solid is considered at the pore-level. The solid, due to coupling with the fluid, material nonlinearities, and macroscopic boundary conditions, can deform enough so that the pore-space is altered significantly. As a result, macroscopic properties such as the permeability of the porous media become nonlinearly dependent on the fine-scale displacements. Therefore, classical upscaled models, such as Biot's equations, can no longer be applied. We propose a series of numerical upscaling models in the context of the Multiscale Finite Element Method (MsFEM) which couple this fine-scale FSI problem to a nonlinear elliptic equation for the averaged pressure and displacements at the coarse scale. The proposed MsFEM schemes correctly transfer the appropriate physics from the fine to the coarse scale. Several numerical examples which demonstrate the methods are also presented.

Original languageEnglish (US)
Title of host publicationLarge-Scale Scientific Computing - 7th International Conference, LSSC 2009, Revised Papers
Pages148-156
Number of pages9
Volume5910 LNCS
DOIs
StatePublished - 2010
Externally publishedYes
Event7th International Conference on Large-Scale Scientific Computations, LSSC 2009 - Sozopol, Bulgaria
Duration: Jun 4 2009Jun 8 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5910 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Conference on Large-Scale Scientific Computations, LSSC 2009
CountryBulgaria
CitySozopol
Period06/4/0906/8/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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