Effective equations for fluid-structure interaction with applications to poroelasticity

Handle URI:
http://hdl.handle.net/10754/562400
Title:
Effective equations for fluid-structure interaction with applications to poroelasticity
Authors:
Brown, Donald; Popov, Peter V.; Efendiev, Yalchin R. ( 0000-0001-9626-303X )
Abstract:
Modeling of fluid-solid interactions in porous media is a challenging and computationally demanding task. Due to the multiscale nature of the problem, simulating the flow and mechanics by direct numerical simulation is often not feasible and an effective model is preferred. In this work, we formally derive an effective model for Fluid-Structure Interaction (FSI). In earlier work, assuming infinitesimal pore-scale deformations, an effective poroelastic model of Biot was derived. We extend this model to a nonlinear Biot model that includes pore-scale deformation into the effective description. The main challenge is the difference in coordinate systems of the fluid and solid equations. This is circumvented by utilizing the Arbitrary Lagrange-Eulerian (ALE) formulation of the FSI equations, giving a unified frame in which to apply two-scale asymptotic techniques. In the derived nonlinear Biot model, the local cell problem are coupled to the macroscopic equations via the effective coefficients. These coefficients may be viewed as tabular functions of the macroscopic parameters. After simplifying this dependence, we assume the coefficients depend on macroscopic pressure only. Using a three dimensional pore geometry we calculate, as a proof-of-concept example, the effective permeability and Biot coefficients for various values or pressure. We observe that, for this geometry, a stronger pressure dependence on flow quantities than on mechanically based effective quantities. © 2014 Taylor & Francis Group, LLC.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Informa UK Limited
Journal:
Applicable Analysis
Issue Date:
5-Nov-2012
DOI:
10.1080/00036811.2013.839780
Type:
Article
ISSN:
00036811
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBrown, Donalden
dc.contributor.authorPopov, Peter V.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.date.accessioned2015-08-03T10:03:51Zen
dc.date.available2015-08-03T10:03:51Zen
dc.date.issued2012-11-05en
dc.identifier.issn00036811en
dc.identifier.doi10.1080/00036811.2013.839780en
dc.identifier.urihttp://hdl.handle.net/10754/562400en
dc.description.abstractModeling of fluid-solid interactions in porous media is a challenging and computationally demanding task. Due to the multiscale nature of the problem, simulating the flow and mechanics by direct numerical simulation is often not feasible and an effective model is preferred. In this work, we formally derive an effective model for Fluid-Structure Interaction (FSI). In earlier work, assuming infinitesimal pore-scale deformations, an effective poroelastic model of Biot was derived. We extend this model to a nonlinear Biot model that includes pore-scale deformation into the effective description. The main challenge is the difference in coordinate systems of the fluid and solid equations. This is circumvented by utilizing the Arbitrary Lagrange-Eulerian (ALE) formulation of the FSI equations, giving a unified frame in which to apply two-scale asymptotic techniques. In the derived nonlinear Biot model, the local cell problem are coupled to the macroscopic equations via the effective coefficients. These coefficients may be viewed as tabular functions of the macroscopic parameters. After simplifying this dependence, we assume the coefficients depend on macroscopic pressure only. Using a three dimensional pore geometry we calculate, as a proof-of-concept example, the effective permeability and Biot coefficients for various values or pressure. We observe that, for this geometry, a stronger pressure dependence on flow quantities than on mechanically based effective quantities. © 2014 Taylor & Francis Group, LLC.en
dc.publisherInforma UK Limiteden
dc.subjectFSIen
dc.subjectmultiscaleen
dc.subjectporoelasticityen
dc.titleEffective equations for fluid-structure interaction with applications to poroelasticityen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalApplicable Analysisen
dc.contributor.institutionInstitute for Parallel Processing, Bulgarian Academy of Sciences, Sofia, 1113, Bulgariaen
dc.contributor.institutionDepartment of Mathematics, Texas AandM University, College Station, TX, 77843, United Statesen
kaust.authorBrown, Donalden
kaust.authorEfendiev, Yalchin R.en
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