Conservative one-dimensional finite volume discretization of a new cavitation model for piston–ring lubrication

This paper presents a conservative numerical implementation of a new cavitation model that is well suited for lubrication problems with cavitated regions in which the fluid film is attached to just one of the participating surfaces, as happens for instance in piston–ring assemblies. This new model was recently proposed by Buscaglia et al. (2011) and is the first successful attempt at modifying the Elrod–Adams model considering a physically realistic value for the lubricant transport velocity in the incomplete-film region in those cases. In this work we show first the reasons for previous attempts to have failed, which come from a loss of uniqueness of the associated exact mathematical problem. Then, the new model is briefly recalled and a one dimensional numerical implementation by means of a finite volume scheme is presented together with several test-case results.