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When a discretized Reynolds equation is to be solved iteratively at least three subjects have to be determined first. These are the iterative solution method, the size of gridwork for the numerical model, and the stopping criterion for the iterative computing. The truncation error analysis of the Reynolds equation is used to provide the stopping criterion, as well as to estimate an adequate grid size based on a required relative precision or grid convergence index. In the simulated lubrication analyses, the convergent rate of the solution is further improved by combining a simple multilevel computing, the modified Chebyshev acceleration, and multithreaded computing. The best case is obtained by using the parallel three-level red-black successive-over-relaxation (SOR) with Chebyshev acceleration. The speedups of the best case relative to the case using sequential SOR with optimal relaxation factor are around 210 and 135, respectively, for the slider and journal bearing simulations.

The study reported in this paper deals with the development of a thermohydrodynamic computational procedure for evaluating the pressure, temperature and velocity distributions in fluid films with fixed geometry between the stationary and moving bearing surfaces. The velocity variations and the heat generation are assumed to occur in a central zone with the same length and width as the bearing but with a significantly smaller thickness than the fluid film thickness. The thickness of the heat generation (shear) zone is developed empirically for the best fit with experimentally determined peak pressures for a journal bearing with a fixed film geometry operating in the laminar regime. A transient thermohydrodynamic computational model with a transformed rectangular computational domain is utilized. The analysis can be readily applied to any given film geometry. The computed distribution of the pressure in the film is in excellent agreement with the experimental findings for different oils and speeds. The developed procedure gives an analytical basis for explaining the “Fogy effect” where significant pressures can be generated in slider bearings with parallel surfaces as a result of the thermal expansion of the film in the direction of the thickness. The procedure confirms the experimentally determined square root relationship between the pressure and the sliding velocity reported in references [1–4]. The normalized pressure profiles computed for the different conditions of the journal bearings are identical to those obtained by isoviscous theory.

This study presents an efficacy comparison of iterative solution methods for solving the compressible-fluid Reynolds equation in modeling air- or gas-lubricated bearings. A direct fixed-point iterative (DFI) method and Newton’s method are employed to transform the Reynolds equation in a form that can be solved iteratively. The iterative solution methods examined are the Gauss–Seidel method, the successive over-relaxation (SOR) method, the preconditioned conjugate gradient (PCG) method, and the multigrid method. The overall solution time is affected by both the transformation method and the iterative method applied. In this study, Newton’s method shows its effectiveness over the straightforward DFI method when the same iterative method is used. It is demonstrated that the use of an optimal relaxation factor is of vital importance for the efficiency of the SOR method. The multigrid method is an order faster than the PCG and optimal SOR methods. Also, the multigrid and PCG methods involve an extended coding work and are less flexible in dealing with gridwork and boundary conditions. Consequently, a compromise has to be made in terms of ease of use as well as programming effort for the solution of the compressible-fluid Reynolds equation.