In this paper, we analyze the impact of the cavitation model on the numerical assessment of lubricated journal bearings. We compare results using the classical Reynolds model and the so-called $p-θ$ model proposed by Elrod and Adams [1974, “A Computer Program for Cavitation and Saturation Problems ,” Proceedings of the First LEEDS-LYON Symposium on Cavitation and Related Phenomena in Lubrication, Leeds, UK] to fix the lack of mass conservation of Reynolds’ model. Both models are known to give quite similar predictions of load-carrying capacity and friction torque in nonstarved conditions, making Reynolds’ model the preferred model for its better numerical behavior. Here, we report on numerical comparisons of both models in the presence of microtextured bearing surfaces. We show that in the microtextured situation, Reynolds’ model largely underestimates the cavitated area, leading to inaccuracies in the estimation of several variables, such as the friction torque. This dictates that only mass-conserving models should be used when dealing with microtextured bearings.

An average Reynolds equation for predicting the effects of deterministic periodic roughness, taking Jakobsson, Floberg, and Olsson mass flow preserving cavitation model into account, is introduced based upon the double scale analysis approach. This average Reynolds equation can be used both for a microscopic interasperity cavitation and a macroscopic one. The validity of such a model is verified by numerical experiments both for one-dimensional and two-dimensional roughness patterns.

In this paper, it is shown how vaporous cavitation in lubricant films can be modeled in a physically justified manner through the constitutive (compressibility) relation of the fluid. The method treats the flow as a homogeneous mixture employing a “void fraction” variable to quantify the intensity of cavitation. It has been already proposed to study cavitation in fluid mechanics. It is shown how the widely used Jakobsson–Floberg–Olsson (JFO) / Elrod–Adams (EA) mass flow conservation model can be compared with this new model. Moreover, the new model can incorporate the variation of the viscosity in the cavitation region and allows the pressure to fall below a cavitation pressure. Numerical computations show that discrepancy with JFO/EA is mostly associated with light loading condition, starved situation or viscosity effects.

In this paper, the convergence of a Neumann-Dirichlet algorithm to approximate Coulomb's contact problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.

The present paper deals with viscoelastic flows in a thin domain. In particular, we derive and analyse the asymptotic equations of the Stokes-Oldroyd system in thin films (including shear effects). We present a numerical method which solves the corresponding problem and we present some related numerical tests which evidence the effects of the elastic contribution on the flow.