A new mass-conserving formulation of the Reynolds equation is developed using the concept of complementarity. This new method overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. Validation against a number of analytical and semi-analytical formulations, for a variety of problems including textured bearings and squeeze film dampers, is performed. The current formulation is shown to be in very good agreement with existing analytical and numerical mass-conserving solutions.

This contribution presents the development of a general discretization scheme for the solution of Reynolds equation with a mass-conserving cavitation model and its application for the numerical simulation of lubricated contacts to be discretized using irregular grids. Such scheme is based on a hybrid-type formulation, here named as element-based finite volume method that combines the flexibility of the FEM to deal with unstructured grids, while preserving the local and global fluid-flow conservation aspect of the FVM throughout the discretized domain. The accuracy and robustness of the method are successfully tested using several benchmark cases proposed in the recent literature. Simulations of fully or partially textured sliding bearings are finally employed to show the advantages of being able to adopt irregular meshes both in terms of flexibility for the discretization of complex surface features and computational speed.