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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, [email protected].
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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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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).