Coupling nonlinear Stokes and Darcy flow using mortar finite elements

Handle URI:
http://hdl.handle.net/10754/561904
Title:
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
Authors:
Ervin, Vincent J.; Jenkins, Eleanor W.; Sun, Shuyu ( 0000-0002-3078-864X )
Abstract:
We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computational Transport Phenomena Lab
Publisher:
Elsevier BV
Journal:
Applied Numerical Mathematics
Issue Date:
Nov-2011
DOI:
10.1016/j.apnum.2011.08.002
Type:
Article
ISSN:
01689274
Appears in Collections:
Articles; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorErvin, Vincent J.en
dc.contributor.authorJenkins, Eleanor W.en
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2015-08-03T09:33:45Zen
dc.date.available2015-08-03T09:33:45Zen
dc.date.issued2011-11en
dc.identifier.issn01689274en
dc.identifier.doi10.1016/j.apnum.2011.08.002en
dc.identifier.urihttp://hdl.handle.net/10754/561904en
dc.description.abstractWe study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.en
dc.publisherElsevier BVen
dc.subjectCoupled Stokes and Darcy flowen
dc.subjectDefective boundary conditionen
dc.subjectGeneralized nonlinear Stokes flowen
dc.titleCoupling nonlinear Stokes and Darcy flow using mortar finite elementsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.identifier.journalApplied Numerical Mathematicsen
dc.contributor.institutionDepartment of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, United Statesen
kaust.authorSun, Shuyuen
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