Parallel Iterative Methods for the Solution of Fluid-Film Lubrication Models

Solutions of various Reynolds equations are usually required in many fluid-film lubrication analyses. These equations include the nonlinear compressible-fluid Reynolds equation and the generalized Reynolds equation that considers the effect of three-dimensional variation of lubricant viscosity. Because these equations have no theoretical solutions, the solutions for these equations rely on some efficient numerical methods. In some case, for example, when a nonlinear lubrication model is to be optimized an effective numerical method should be able to solve the problem efficiently. While Reynolds equations have been applied and solved frequently, the usual solution method is a simple iterative scheme of relaxation type, such as the over-relaxation method. Up to now some efficient iterative methods and parallel computing are not widely applied in tribological study. Also, a standardized stopping criterion for iterative methods is required to assess the effectiveness of iterative methods. In this proposed two-year project the progress of the study can be divided into four stages. The main objectives of each stage are: (1) Establish the stopping criterion for the iterative methods, which is to be used for efficiency comparison; (2) Compare the computing efficiency when the incompressible-fluid Reynolds equation is solved by the iterative methods. These methods are Gauss-Seidel method, conjugate gradient (with or without preconditioner) method, and multigrid method (for the linear and nonlinear Reynolds equations); (3) Compare the computing efficiency of the iterative methods for solving the compressible fluid Reynolds equation; (4) Implement parallel computing and compare the effectiveness of the parallel iterative methods. The stages (1) and (2) are expected to be completed in the first year of the project, and the stages (3) and (4) are to be completed in the second year. The author has conducted fluid-film lubrication analysis and parallel computing for many years. Incorporating the new development of computing technology and the support from the NSC project funding, the comparison of the iterative methods for various Reynolds equations in terms of efficiency and effectiveness can be established. The results of this study are to be published in the Tribology related journals.

Project ID:PB9907-10768
External Project ID:NSC99-2221-E182-014