×

zbMATH — the first resource for mathematics

Une méthode du type caractéristique pour la résolution d’un problème de lubrification hydrodynamique en régime transitoire. (A method of characteristics for the resolution of a time-dependent lubrication problem in hydrodynamics). (French) Zbl 0748.76040
The authors study a moving free boundary problem related to a cavitation model in a lubricated device. In this case, the classical Reynolds equation includes a new variable acting as saturation. The authors introduce an algorithm based on the characteristic method for the time discretization. In this way, the time-discretized problem can be viewed as a variational inequality in which the saturation acts as a Lagrange multiplier. Finally, some specific numerical computations are given for a face seals device.

MSC:
76D08 Lubrication theory
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] G. BAYADA, M. CHAMBAT. Existence and uniqueness for a lubrication problem with non regular conditions on the free boundary, Boll. un Math. Ital., 6, 3B, 543-547 (1984). Zbl0612.35026 MR762718 · Zbl 0612.35026
[2] G. BAYADA, M. CHAMBAT, Sur quelques modélisations de la zone de cavitation en lubrification hydrodynamique, Journal de Méc. Théor. Appl., vol. 5, 5, 703-729 (1986). Zbl0621.76030 MR878123 · Zbl 0621.76030
[3] A. BERMUDEZ, J. DURANY, La méthode des caractéristiques pour les problèmes de convection diffusion stationnaires, RAIRO Modél. Math. Anal. Numér., 21, 1, 7-26 (1987). Zbl0613.65121 MR882685 · Zbl 0613.65121
[4] M. BOUKROUCHE, M. EL ALAOUI, G. BAYADA, Generalized Hele Shaw type problems, Rap. int. URA 740 Analyse Num. Lyon, 1989.
[5] D. E. BREWE, Theoretical Modeling of Vapor Cavitation in Dynamically loaded Journal Bearing, ASME J. of Tribology, 108, 628-638 (1986).
[6] J. CEA, Optimisation, théorie et algorithmes, Dunod, Paris, 1971. Zbl0211.17402 MR298892 · Zbl 0211.17402
[7] A. B. CROWLEY, On the weak solution of moving boundary problems, J. Inst. Math. Applics., 24, 43-57 (1979). Zbl0416.65073 MR539372 · Zbl 0416.65073
[8] A. DEGUEIL, Résolution par une méthode d’éléments finis d’un problème de Stefan en termes de température et teneur en matériau non gelé, Thèse, Univ. Bordeaux, 1977.
[9] M. EL ALAOUI TALIBI, Sur un problème à frontière libre en mécanique des films minces, Thèse, Univ. Lyon 1, 1986.
[10] C. M. ELLIOT, On a finite approximation of an elliptic variational inequality arising from an implicit time discretization of the Stefan problem, I.M.A., J. Num. Anal. (1981). Zbl0469.65042 · Zbl 0469.65042
[11] H. G. ELROD, A cavitation algorithm, J. of Lubrication Technology, 103, 350-354 (1981).
[12] B. FANTINO, J. FRENES, M. GODET, Conditions d’utilisation de l’équation de Reynolds en mécanique des films minces, série A, C.R. Acad. Sci., Paris, 262, 691-693 (1971). Zbl0217.25202 · Zbl 0217.25202
[13] R. GLOWINSKI, J. L. LIONS, R. TRÉMOLIÈRES, Analyse numérique des inéquations variationnelles, Dunod, 1976. Zbl0358.65091 · Zbl 0358.65091
[14] R. HAARDT, Les joints d’étanchéité à faces radiales : les effets transitoires introduits en lubrification hydrodynamique par leur mésalignement, Thèse, Univ. Lyon 1, 1975.
[15] M. LOHOU, Hydrodynamique des joints d’étanchéité du type radial, Thèse, Univ. Lyon 1, 1972.
[16] P. PIETRA, An upwind finite element method for a filtration, RAIRO Modél. Math. Anal Numér., 16, 4, 463-481 (1982). Zbl0506.76095 MR684833 · Zbl 0506.76095
[17] O. PIRONNEAU, On the transport diffusion algorithm and its application on the Navier Stokes equations, Numer. Math., 38, 309-332 (1981). Zbl0505.76100 MR654100 · Zbl 0505.76100
[18] G. STAMPACHA, D. KINDERLEHRER, An introduction to variational inequalities and applications, Academic Press. 1980. Zbl0457.35001 · Zbl 0457.35001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.