An Arbitrary Lagrangian-Eulerian Formulation for Modelling Cavitation in the Elastohydrodynamic Lubrication of Line Contacts

In this article an arbitrary Lagrangian-Eulerian (ALE) formulation for modelling cavitation in elastohydrodynamic lubrication (EHL) is derived and applied to line contact geometry. The method is developed in order to locate the position of cavitation onset along the length of the contacting region which gives the transition from liquid to vapour in the fluid. The ALE is implemented by introducing a spatial frame of reference in which the solution is required and a material frame of reference in which the governing equations are solved. The spatial frame is moved from the material frame according to the error in the Neumann pressure gradient constraint required at the cavitation location when Dirichlet constraints are imposed for pressure in the liquid phase. Results are calculated under both steady-state and transient operating conditions using a multigrid solver. The solutions obtained are compared to established literature and conventional approaches to modelling cavitation which show that the ALE formulation is an alternative, straightforward and accurate means of implementing such conditions in EHL. This is achieved without the penalties associated with the numerical modelling of Heaviside functions or free boundaries.