Hostname: page-component-6766d58669-kl59c Total loading time: 0 Render date: 2026-05-21T06:35:10.985Z Has data issue: false hasContentIssue false
  • English
  • Français

Stick-slip transition capturing by usingan 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.
Get access

Abstract

The numerical modeling of the fully developed Poiseuille flowof a Newtonian fluid in a square section withslip 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 describingthe slip yield effect, from a full slip to a full stick flow regime.The resolution of variational inequalitiesdescribing the flow is based on the augmented Lagrangian method and afinite element method. The localization of thestick-slip transition points is approximated by ananisotropic auto-adaptive mesh procedure.The singular behavior of the solution at the neighborhood of thestick-slip transition point is investigated.

Keywords

Slip boundary conditionstick-slip problemvariational inequalitiesadaptive meshcomputational fluid mechanics.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 2 , March 2004 , pp. 249 - 260
Copyright
© EDP Sciences, SMAI, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

R.A. Adams, Sobolev spaces. Academic Press (1975).
Borouchaki, H., George, P.L., Hecht, F., Laug, P. and Saltel, E., Delaunay mesh generation governed by metric specifications. Part I: Algorithms. Finite Elem. Anal. Des. 25 (1997) 61–83. CrossRef
F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Verlag (1991).
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).
Fortin, A., Côté, D. and Tanguy, P.A., On the imposition of friction boundary conditions for the numerical simulation of Bingham fluid flows. Comput. Meth. Appl. Mech. Engrg. 88 (1991) 97–109. CrossRef
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).
R. Glowinski, J.L. Lions and R. Trémolières, Numerical analysis of variational inequalities. North Holland, Amsterdam (1981).
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).
F. Hecht, Bidimensional anisotropic mesh generator. INRIA (1997). http://www-rocq.inra.fr/gamma/cdrom/www/bamg
Ionescu, I.R. and Vernescu, B., A numerical method for a viscoplastic problem. An application to the wire drawing. Int. J. Engrg. Sci. 26 (1988) 627–633. CrossRef
N. Kikuchi and J.T. Oden, Contact problems in elasticity: A study of variational inequalities and finite element methods. SIAM Stud. Appl. Math. (1988).
Roquet, N. and Saramito, P., An adaptive finite element method for Bingham fluid flows around a cylinder. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3317–3341. CrossRef
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.
Saramito, P. and Roquet, N., An adaptive finite element method for viscoplastic fluid flows in pipes. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5391–5412. CrossRef
P. Saramito and N. Roquet, Rheolef home page. http://www-lmc.imag.fr/lmc-edp/Pierre.Saramito/rheolef/ (2002).
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
M.G. Vallet, Génération de maillages anisotropes adaptés. Application à la capture de couches limites. Rapport de Recherche No. 1360, INRIA (1990).