Stick-slip transition capturing by using an adaptive finite element method
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, p. 249-260

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.

DOI : https://doi.org/10.1051/m2an:2004012
Classification:  65N22,  65N30,  65N50,  65Z05,  90C46
Keywords: slip boundary condition, stick-slip problem, variational inequalities, adaptive mesh, computational fluid mechanics
@article{M2AN_2004__38_2_249_0,
     author = {Roquet, Nicolas and Saramito, Pierre},
     title = {Stick-slip transition capturing by using an adaptive finite element method},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {2},
     year = {2004},
     pages = {249-260},
     doi = {10.1051/m2an:2004012},
     zbl = {1130.76368},
     mrnumber = {2069146},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_2_249_0}
}
Roquet, Nicolas; Saramito, Pierre. Stick-slip transition capturing by using an adaptive finite element method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, pp. 249-260. doi : 10.1051/m2an:2004012. http://www.numdam.org/item/M2AN_2004__38_2_249_0/

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