Stick-slip transition capturing by using an adaptive finite element method

Nicolas Roquet; Pierre Saramito

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 38, Issue: 2, page 249-260
  • ISSN: 0764-583X

Abstract

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The numerical modeling of the fully developed Poiseuille flow of a Newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the augmented Lagrangian method and a finite element method. The localization of the stick-slip transition points is approximated by an anisotropic auto-adaptive mesh procedure. The singular behavior of the solution at the neighborhood of the stick-slip transition point is investigated.

How to cite

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Roquet, Nicolas, and Saramito, Pierre. "Stick-slip transition capturing by using an adaptive finite element method." ESAIM: Mathematical Modelling and Numerical Analysis 38.2 (2010): 249-260. <http://eudml.org/doc/194213>.

@article{Roquet2010,
abstract = { The numerical modeling of the fully developed Poiseuille flow of a Newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the augmented Lagrangian method and a finite element method. The localization of the stick-slip transition points is approximated by an anisotropic auto-adaptive mesh procedure. The singular behavior of the solution at the neighborhood of the stick-slip transition point is investigated. },
author = {Roquet, Nicolas, Saramito, Pierre},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Slip boundary condition; stick-slip problem; variational inequalities; adaptive mesh; computational fluid mechanics.},
language = {eng},
month = {3},
number = {2},
pages = {249-260},
publisher = {EDP Sciences},
title = {Stick-slip transition capturing by using an adaptive finite element method},
url = {http://eudml.org/doc/194213},
volume = {38},
year = {2010},
}

TY - JOUR
AU - Roquet, Nicolas
AU - Saramito, Pierre
TI - Stick-slip transition capturing by using an adaptive finite element method
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 2
SP - 249
EP - 260
AB - The numerical modeling of the fully developed Poiseuille flow of a Newtonian fluid in a square section with slip yield boundary condition at the wall is presented. The stick regions in outer corners and the slip region in the center of the pipe faces are exhibited. Numerical computations cover the complete range of the dimensionless number describing the slip yield effect, from a full slip to a full stick flow regime. The resolution of variational inequalities describing the flow is based on the augmented Lagrangian method and a finite element method. The localization of the stick-slip transition points is approximated by an anisotropic auto-adaptive mesh procedure. The singular behavior of the solution at the neighborhood of the stick-slip transition point is investigated.
LA - eng
KW - Slip boundary condition; stick-slip problem; variational inequalities; adaptive mesh; computational fluid mechanics.
UR - http://eudml.org/doc/194213
ER -

References

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  15. P. Saramito and N. Roquet, Rheolef home page. (2002).  URIhttp://www-lmc.imag.fr/lmc-edp/Pierre.Saramito/rheolef/
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