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

Nicolas Roquet; Pierre Saramito

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2004)

  • 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 - Modélisation Mathématique et Analyse Numérique 38.2 (2004): 249-260. <http://eudml.org/doc/244800>.

@article{Roquet2004,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {slip boundary condition; stick-slip problem; variational inequalities; adaptive mesh; computational fluid mechanics},
language = {eng},
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/244800},
volume = {38},
year = {2004},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2004
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/244800
ER -

References

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  1. [1] R.A. Adams, Sobolev spaces. Academic Press (1975). Zbl0314.46030MR450957
  2. [2] H. Borouchaki, P.L. George, F. Hecht, P. Laug and E. Saltel, Delaunay mesh generation governed by metric specifications. Part I: Algorithms. Finite Elem. Anal. Des. 25 (1997) 61–83. Zbl0897.65076
  3. [3] F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Verlag (1991). Zbl0788.73002MR1115205
  4. [4] F. Brezzi, M. Fortin and R. Stenberg, Error analysis of mixed-interpolated elements for Reissner-Mindlin plates. Research Repport No. 780, Instituto di Analisi Numerica, Pavie (1991). Zbl0751.73053MR1115287
  5. [5] A. Fortin, D. Côté and P.A. Tanguy, On the imposition of friction boundary conditions for the numerical simulation of Bingham fluid flows. Comput. Meth. Appl. Mech. Engrg. 88 (1991) 97–109. Zbl0745.76067
  6. [6] M. Fortin and R. Glowinski, Méthodes de lagrangien augmenté. Applications à la résolution numérique de problèmes aux limites. Méthodes Mathématiques de l’Informatique, Dunod (1982). Zbl0491.65036
  7. [7] R. Glowinski, J.L. Lions and R. Trémolières, Numerical analysis of variational inequalities. North Holland, Amsterdam (1981). Zbl0463.65046MR635927
  8. [8] J. Haslinger, I. Hlavàček and J. Nečas, Numerical methods for unilateral problems in solidmechanics. P.G. Ciarlet and J.L. Lions Eds., Handb. Numer. Anal. IV (1996). Zbl0873.73079MR1422506
  9. [9] F. Hecht, Bidimensional anisotropic mesh generator. INRIA (1997). http://www-rocq.inra.fr/gamma/cdrom/www/bamg 
  10. [10] I.R. Ionescu and B. Vernescu, A numerical method for a viscoplastic problem. An application to the wire drawing. Int. J. Engrg. Sci. 26 (1988) 627–633. Zbl0637.73047
  11. [11] N. Kikuchi and J.T. Oden, Contact problems in elasticity: A study of variational inequalities and finite element methods. SIAM Stud. Appl. Math. (1988). Zbl0685.73002MR961258
  12. [12] N. Roquet and P. Saramito, An adaptive finite element method for Bingham fluid flows around a cylinder. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3317–3341. Zbl1054.76053
  13. [13] N. Roquet, R. Michel and P. Saramito, Errors estimate for a viscoplastic fluid by using P k finite elements and adaptive meshes. C. R. Acad. Sci. Paris, Série I 331 (2000) 563–568. Zbl1011.76047
  14. [14] P. Saramito and N. Roquet, An adaptive finite element method for viscoplastic fluid flows in pipes. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5391–5412. Zbl1002.76071
  15. [15] P. Saramito and N. Roquet, Rheolef home page. http://www-lmc.imag.fr/lmc-edp/Pierre.Saramito/rheolef/ (2002). 
  16. [16] P. Saramito and N. Roquet, Rheolef users manual. Technical report, LMC-IMAG (2002). http://www-lmc.imag.fr/lmc-edp/Pierre.Saramito/rheolef/usrman.ps.gz 
  17. [17] M.G. Vallet, Génération de maillages anisotropes adaptés. Application à la capture de couches limites. Rapport de Recherche No. 1360, INRIA (1990). 

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