An Analysis of the Method of Lines for the Reynolds Equation in Hydrodynamic Lubrication
Copyright policy )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 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.
Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena, free multipoint system of ordinary differential equations, Numerical optimization and variational techniques, line SOR method, Method of lines for boundary value problems involving PDEs, Algorithms for approximation of functions, cavitation boundary conditions, Basic methods in fluid mechanics, Reynolds equation, invariant embedding, hydrodynamic lubrication
Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena, free multipoint system of ordinary differential equations, Numerical optimization and variational techniques, line SOR method, Method of lines for boundary value problems involving PDEs, Algorithms for approximation of functions, cavitation boundary conditions, Basic methods in fluid mechanics, Reynolds equation, invariant embedding, hydrodynamic lubrication
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