An Analysis of the Method of Lines for the Reynolds Equation in Hydrodynamic Lubrication

The Reynolds equation for a hydrodynamic journal bearing is discretized with the method of lines. A continuous analogue of the line SOR iteration is set up to solve the resulting free multipoint system of ordinary differential equations via a sequence of one-dimensional free boundary problems. It is...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 18; no. 1; pp. 165 - 177
Main Author Meyer, Gunter H.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.02.1981
Subjects
Applied mathematics
Boundary conditions
Cavitation
Cavitation flow
Computational mathematics
Convergent boundaries
Embeddings
Hydrodynamics
Initial guess
Journal bearings
Linear equations
Lubrication
Numerical analysis
Ordinary differential equations
Reynolds equation
Variational inequalities
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Summary:The Reynolds equation for a hydrodynamic journal bearing is discretized with the method of lines. A continuous analogue of the line SOR iteration is set up to solve the resulting free multipoint system of ordinary differential equations via a sequence of one-dimensional free boundary problems. It is shown that each one-dimensional problem can be solved with invariant imbedding, that the line SOR method converges, and that the solution of the by-lines discretization converges to the solution of a variational inequality derived from the Reynolds equation
ISSN:0036-1429
1095-7170
DOI:10.1137/0718013