Numerical solution of cavitation problems in lubrication. (English) Zbl 0687.76030

Summary: A combination of the method of characteristics and of the finite element method is applied to solve numerically a stationary free boundary problem of hydrodynamic lubrication with cavitation. The discretization leads to a system of nonlinear equations. To solve it a duality iterative algorithm is used. Numerical results presented.


76D08 Lubrication theory
76M99 Basic methods in fluid mechanics
Full Text: DOI


[1] Alvarez, J., Problemas de frontera libre en teoría de lubrificaión, (Thesis (1986), Department of Applied Mathematics, Univ. Complutense de Madrid: Department of Applied Mathematics, Univ. Complutense de Madrid Spain)
[2] Bayada, G.; Chambat, M., Sur quelques modélisations de la zone de cavitation en lubrification hydrodynamique, J. Theoret. Appl. Mech., 5, 703-729 (1986) · Zbl 0621.76030
[3] Bayada, G.; Chambat, M., Existence and uniqueness for a lubrication problem with nonregular conditions on the free boundary, Boll. UN. Mat. Ital., 3-B, 6, 543-557 (1984) · Zbl 0612.35026
[4] Bermudez, A.; Durany, J., La méthode des caractéristiques pour les problèmes de convection-diffusion stationnaires, Math. Model. Numer. Anal., 21, 7-26 (1987) · Zbl 0613.65121
[5] Bermudez, A.; Durany, J., Application of characteristics method with variable time-step to steady-state convection-diffusion problems, (Ortiz, E., Numerical Approximation of Partial Differential Equations. Numerical Approximation of Partial Differential Equations, Mathematics Studies, 133 (1987), North-Holland: North-Holland Amsterdam), 377-386 · Zbl 0609.65088
[6] Bermudez, A.; Durany, J., Numerical solution of steady-state flow through a porous dam, Comput. Methods Appl. Mech. Engrg., 68, 55-65 (1988) · Zbl 0626.76098
[7] Bermudez, A.; Moreno, C., Duality methods for solving variational inequalities, Comput. Math. Appl., 7 (1981) · Zbl 0456.65036
[8] Cameron, A., Basic lubrication theory, Ellis Horwood Ser. Engrg. Sci. (1983)
[9] Capriz, G.; Cimatti, G., Free boundary problems in the theory of hydrodynamic lubrication: a survey, (Free Boundary Problems: Theory and Applications, Vol. 2 (1983), Pitman: Pitman London) · Zbl 0557.76038
[10] M. Chipot, On the Reynolds lubrication equation, I.M.A. Preprint No. 206, University of Minnesota, Minneapolis (to appear).; M. Chipot, On the Reynolds lubrication equation, I.M.A. Preprint No. 206, University of Minnesota, Minneapolis (to appear).
[11] Lions, J. L., Quelques Méthodes de Resolution des Problèmes aux Limites Non Lineaires (1969), Dunod: Dunod París · Zbl 0189.40603
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