Stabilized Finite Elements for Elastohydrodynamic Lubrication Problems

In this work, we are mainly interested in modelling a particular lubrication regime known as Elastohydrodynamic (EHD). The pressure generated in the conjunction is high enough to induce a significant elastic deformation of the contacting bodies. Therefore a strong coupling between hydrodynamic and elastic effects is involved. A finite element full-system approach is used to model the lubricant flow in such contacts. The hydrodynamic and elastic problems are solved simultaneously by means of a Newton-like procedure. At the exit of the contact, a free boundary problem arises. It is handled by applying a penalty method. For highly loaded contacts, the standard Galerkin solution of the hydrodynamic (Reynolds) equation exhibits an oscillatory behaviour. This is explained by writing it as a convectiondiffusion equation as a function of pressure. When the load is highly increased, this equation becomes convection dominated and requires artificial diffusion techniques in order to stabilize the solution. The classical Reynolds equation assumes the lubricant is a Newtonian fluid. The approach is extended to generalized forms of this equation to account for nonNewtonian and thermal effects. A similar stabilization procedure is used to stabilize their solutions when high loads are considered.