Efficient numerical solution of realistic and, therefore, complex equation systems occupies many researchers in many disciplines. For various reasons, but mainly in order to approximate reality, a very large number of unknowns are needed. Using classical techniques, the solution of such a system of equations would take too long, and so sometimes MultiLevel techniques are used to accelerate convergence. Over the last one and a half decades, the authors have studied the problem of Elastohydrodynamic Lubrication, governed by a complex integro-differential equation. Their work has resulted in a very efficient and stable solver. In this book they describe the different intermediate problems analyzed and solved, and how those ingredients finally come together in the EHL solver. A number of these intermediate problems, such as Hydrodynamic Lubrication and Dry Contact, are useful in their own right. In the Appendix the full codes of the Poisson problem, the Hydrodynamic Lubrication problem, the dry contact solver and the EHL solver are given. These codes are all written in 'C' language, based on the 'ANSI-C' version.
For researchers interested in tribology and wear and in particular to the application of complex integro-differential equations to Elastohydrodynamic Lubrication.
Table of Contents
Introduction Justification. History. Description of the EHL Problem. Simplification. Model Problems. Conclusion. Advanced Topics. Numerical Methods: Introduction Model Problems. Discretization. Systems of Equations. Direct Solver. Iterative Solver. Relaxation. Performance. Local Mode Analysis. Conclusion. Advanced Topics. Multigrid General Principle. Correction Scheme. Intergrid Transfers. Coarse Grid Operator LH Coarse Grid Correction Cycle. Cycle Performance. Full MultiGrid. Full Approxination Scheme. 1d Results. 2d Results. Conclusion. Advanced Techniques. Hydrodynamic Lubrication Equations. Discrete Equations. Relaxation. Caviation and Complementarity. Coarse Grid Correction. Full MultiGrid. Accuracy. Other L/R Ratios: Bearing Design. Conclusion. Advanced Topics. Dry Contact. Equations. Discrete Equations. Relaxation. Coarse Grid Correction. Cycle Performance. Full MultiGrid. Multilevel Multi-Integration. Incorporating MLMI into the FMG Solver. Conclusion. Advanced Topics. Elastohydrodynamic Lubrication. Introduction. Equations. Dimensionless Equations. Dimensionless Parameters. Discrete Equations. Model Problems. Relaxation of the EHL Problem. Coarse Grid Correction Cycle. Full MultiGrid. Design Graphs. Conclusion. Advanced Topics.