A finite element algorithm for cavitation in hydrodynamic lubrication
Keywords:
cavitating fluid film, hydrodynamic lubrication, Reynolds equation, numerical algorithm, finite element analysis, convergence proofsAbstract
Issued from a mass conservation cavitation model for a slightly compressible fluid, a specific finite element discretization and a related fixed-point algorithm are introduced. Convergence of this algorithm is proved. Moreover, the behavior of the solution of the discrete problem towards the solution of the continuous problem is studied. Numerical results are given for one and two-dimensional problems.
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References
[ALT 80] ALT H. W., “Numerical Solution of Steady-State Porous Flow Free Boundary
Problems”, Numer. Math., vol. 36, p. 73-98, 1980.
[BAY 84] BAYADA G., CHAMBAT M., “Existence and Uniqueness for a Lubrication
Problem with non Regular Conditions on the Free Boundary”, BUMI, vol. 6, 3-B, p. 543-
, 1984.
[BAY 86] BAYADA G., CHAMBAT M., « Sur quelques modélisations de la zone de cavitation
en lubrification hydrodynamique », Journal of theoretical & Applied Mechanics, vol. 5,
n° 5, p. 703-709, 1986.
[BAY 90] BAYADA G., CHAMBAT M. & El ALAOUI TALIBI M., “Variational Formulations and
Finite Element Algorithms for Cavitation Problems”, ASME J. of Trib., vol. 112, p. 398-
, 1990.
[BAY 98] BAYADA G., CHAMBAT M. & VAZQUEZ C., “Characteristics Method for the
Formulation and Computation of a Free Boundary Cavitation Problem”, J. of Comp. And
Appl. Math., vol. 98, p 191-212, 1998.
[BON 95] BONNEAU D., GUINES D., FRENE J. & TOPLOSKI J., “EHD Analysis, including
Structural Inertia Effects and a Mass-Conserving Cavitation Model”, ASME J. of Trib.,
vol. 117, p. 540-547, 1995.
[CHA 87] CHAMBAT M., Contribution à la modélisation en lubrification hydrodynamique:
phénomènes de cavitation et études asymptotiques pour un écoulement entre des surfaces
rugueuses, Thèse d’Etat, Mathématiques, Université Lyon 1, 1987.
[CIO 00] CIOC S., KEITH T., “Application of the CE/SE Method to one-dimensional Flow in
Fluid Film Bearing”, Com. at the ASME meeting, Tolède, 2000.
[CRY 71] CRYER C., “The Method of Christopherson for Solving Free Boundary Problems
for infinite Journal Bearings”, Math. Of Comp., vol. 25, 115, p. 435-444, 1971.
[DOW 75] DOWSON D., GODET M., TAYLOR C. M., “Cavitations and related Phenomena in
Lubrication”, Mech. Eng. Publ. Ltd, Londres, 1975.
[ELR 81] ELROD H.G., “A Cavitation Algorithm “, ASME J. of Lubrication Technology, vol.
, p. 350-354, 1981.
[FLO 57] FLOBERG L., JAKOBSON J., “The Finite Journal Bearing considering Vaporization”,
Trans. Chalmers University, vol. 190, Suède, 1957.
[FRE 90] FRENE J., NICOLAS D., DEGUEURCE B., BERTHE D., GODET M., Lubrification
hydrodynamique, Eyrolles, Paris, 1990.
[LUN 69] LUNDHOLM G., “The circumferential Groove Journal Bearing Considering
Cavitation and Dynamic Stability”, Acta Polytechnica Scandinavia, ME series, n° 42,
Stockholm, 1969.
[MUR 74] MURTY K.G., “Note on a Bard-type Scheme for solving the Complementarity
Problems”, Onsearch, vol. 11, p. 123-130, 1974.
[PIE 82] PIETRA P., “An up-wind Finite Element Method for a Filtration Problem”, Numerical
Analysis, RAIRO, vol. 16, 4, p. 463-481, 1982.
[VIJ 89] VIJAYARAGHAVAN D., KEITH T.G., “Development and Evaluation of a Cavitation
Algorithm”, Tribology Trans. , vol. 32, 2, p. 225-233, 1989.
