Numerical computation of free boundary problems in elastohydrodynamic lubrication

Abstract An alternative algorithm has been developed for computing the behavior of thin fluid films in two elastohydrodynamic lubrication problems. The presence of elasticity, lubrication, and cavitation leads to a nonlinear coupled system of partial differential equations. The hydrodynamic part of both problems is governed by the well-known Reynolds equation combined with the cavitation model of Elrod-Adams, which motivates the appearance of a free boundary. Elastic deformations are taken into account by means of the Hertz equation in rolling ball contact problems or the elastic hinged plate biharmonic equation in the case of journal-bearing devices with thin bearing. A numerical method decoupling the hydrodynamic part of the problem and the elastic one is presented. This method also involves an upwind scheme to discretize the lubrication model and finite element approximations.

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