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Technical Briefs

Fast Convergence of Iterative Computation for Incompressible-Fluid Reynolds Equation

[+] Author and Article Information
Nenzi Wang

Department of Mechanical Engineering,  Chang Gung University, 259 Wen-Hwa 1st Road, Tao-Yuan 333, Taiwannenzi@mail.cgu.edu.tw

Kuo-Chiang Cha

Department of Mechanical Engineering,  Chang Gung University, 259 Wen-Hwa 1st Road, Tao-Yuan 333, Taiwanckc001@mail.cgu.edu.tw

Hua-Chih Huang

 Mechanical and Systems Research Laboratories,  Industrial Technology Research Institute, No. 191, Gung Ye 38 Road, Taichung Industrial Area, Tai-Chung 407, TaiwanHuaChih.Huang@itri.org.tw

J. Tribol 134(2), 024504 (Apr 12, 2012) (4 pages) doi:10.1115/1.4006360 History: Received January 18, 2012; Revised March 05, 2012; Published April 11, 2012; Online April 12, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 4

Dimensionless peak pressure of the journal bearing versus the number of iteration

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Figure 3

Dimensionless peak pressure of the slider versus the number of iteration

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Figure 2

Numerical solution and estimated true solution of the dimensionless average pressure of the journal bearing (ε = 0.9)

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Figure 1

Numerical solution and estimated true solution of the dimensionless average pressure of the slider (1≤h¯≤5)

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