Mixed formulation and finite element treatment of the mass-conserving cavitation model

A mixed formulation of the mass-conserving cavitation model is developed. The cavitation problem is formulated in terms of the hydrodynamic pressure and a complementary variable representing the void fraction in the cavitation zone. Weak form of the mass-balance equation is consistently derived, and it exhibits subtle differences with respect to the available formulations. Finite element treatment preserves the two-field formulation, and a semi-smooth Newton method is applied to solve the resulting discretized equations. A monolithic Newton-based scheme is also applied to solve the fully coupled elastohydrodynamic lubrication problem in the soft-EHL regime. Numerical examples illustrate the performance of the computational scheme.