Summary
The stationary Reynolds equation is solved over a rectangular region. The problem is linearized by Picard linearization. The ADI method is used to solve the resulting set of linear equations. A set of parameters is introduced to speed up convergence as well for the Picard linearization as for the ADI method. A comparison is made with Booy-Coleman's method. Results are given for bearing numbers 10 to 1000.
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References
V. Castelli and J. Pirvics, Review of Numerical Methods in Gas Bearing Film Analysis,Journal of Lubrication Technology, Trans. ASME, Series F, 90, 4 (1968) 777–792.
M. L. Booy, A Non iterative Solution of Poisson's and Laplace's Equations With Application to Slow Viscous Flow,Journal of basic Engineering, Trans. ASME, Series D, 88, 4 (1966) 725–733.
R. Coleman, The Numerical Solution of Linear Elliptic Equations,Journal of Lubrication Technology, Trans. ASME, Series F, 90, 4 (1968) 773–776.
R. S. Varga,Matrix Iterative Analysis, Prentice Hall, New York (1962).
I. C. Tang, The Design and Analysis of Rectangular Gas Slider Bearings,Wear, 20 (1972) 59–65. 4.
J. Douglas, jr., Alternating Direction Iteration for Mildly Nonlinear Elliptic Difference Equations,Numerische Math., 3 (1961) 92–98.
A. Friedman,Partial Differential Equations, Holt, Rinehart and Winston Inc. (1969).
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The author is indebted to Prof. P. J. Zandbergen, Mr. van Beckum and Mr. van Eck of this institute.
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De Vries, R.W. An alternating direction (ADI) method for a self-acting rectangular gas bearing. J Eng Math 9, 71–79 (1975). https://doi.org/10.1007/BF01535499
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DOI: https://doi.org/10.1007/BF01535499