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

Published online by Cambridge University Press:  15 March 2004

Nicolas Roquet  and
Pierre Saramito
Nicolas Roquet
Affiliation:
LMC-IMAG, BP 53, 38041 Grenoble Cedex 9, France.
Pierre Saramito
Affiliation:
LMC-IMAG, BP 53, 38041 Grenoble Cedex 9, France, Pierre.Saramito@imag.fr.
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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.

Keywords

Slip boundary conditionstick-slip problemvariational inequalitiesadaptive meshcomputational fluid mechanics.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 2 , March 2004 , pp. 249 - 260
Copyright
© EDP Sciences, SMAI, 2004

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