A GENERAL FINITE VOLUME METHOD SOLUTION FOR THE REYNOLDS LUBRICATION EQUATION WITH MASS-CONSERⅥNG CAⅥTATION MODEL

摘要

The numerical solution of the Reynolds equation for realistic lubrication applications are traditionally obtained by using the Finite Difference Method (FDM), which in turn has proven to be robust enough to cope with the uncomplicated, regularly discretized domains usually found in conventional lubricated components, e.g. journal and sliding bearings, piston rings etc. On the other hand, whenever more complex geometries are involved, and so the necessity of considering unstructured grids to properly discretize the solution domains, both the Finite Element Method (FEM) as well as the Finite Volume Method (FVM) are employed for the numerical calculations. However, when mass conservation is contemplated in the fluid-film cavitation modelling by the imposition of the so-called JFO (Jakobsson, Floberg and Olsson) conditions. the solution of the associated modified diffusion-convection Reynolds equation (see e.g. the p - θ Elrod-Adams model) is not straightforwardly accomplished with the FEM formulation (essentially due to difficulties in the discretization of the convective term). In contrast, the intrinsic conservative nature of the FVM automatically satisfy the local and global flow conservation, and hence the complementary JFO conditions, throughout the lubricated domain; the discretization of the convective term is performed by upwind-based scheme. The only disadvantage of conventional FVM schemes is the absence of a standardized strategy to deal with unstructured meshes, which is a prerogative of the FEM.