An In-depth Investigation of the Multigrid Approach to Steady and Transient EHL Problems

Multigrid methods have proved robust and highly desirable in terms of the iteration speed in solving elastohydrodynamic lubrication (EHL) problems. Lubrecht, Venner and Ehret, amongst others, have shown that multigrid can be successfully used to obtain converged solutions for steady problems. steady problems. A detailed study reinforces these results but also shows, in some cases, that while multigrid techniques give initial rapid convergence, the residuals having dropped to a low level may reach a stalling point, mainly due to the cavitation region. The study will explain this behaviour in terms of the iterative scheme and show how, if this happens, the errors in the fine grid solution can be reduced further. Example results of both steady and transient EHL problems (including a thermal viscoelastic case) are shown with further developments into adaptive meshes considered.