Multigrid techniques: a fast and efficient method for the numerical simulation of elastohydrodynamically lubricated point contact problems

The introduction and further development of algorithms based on multigrid (multilevel) techniques has resulted in fast and efficient solvers for elastohydrodynamically lubricated (EHL) point contact problems. As a result the capability to simulate steady state and transient point contact problems numerically has greatly increased in the past decade. This has led to an increased understanding of the mechanisms controlling film formation and pressure in the contact in relation to the operating conditions. In this article an overview is given of the essential ingredients of an efficient multigrid algorithm for an EHL point contact problem. Results are presented for some characteristic problems that illustrate today's numerical simulation capability. It is concluded that, with respect to EHL, one of the main questions of the last part of the century has been answered, i.e. how to solve efficiently the modelling equations such that realistic and highly loaded situations can be simulated. The challenge that researchers and engineers now face is how to translate the new insights into simple rules for design and engineering, and to establish clearly the limits of validity of the models that are used in simulations both on the scale of the contact as a whole as well as on a subcontact scale