Some aspects of lubrication in heavy regimes: Thermal effects, stability and turbulence

In this work, a combination of numerical methods applied to thermohydrodynamic lubrication problems with cavitation is presented. It should be emphasized the difficulty of the nonlinear mathematical coupled model involving a free boundary problem, but also the simplicity of the algorithms employed to solve it. So, finite element discretizations for the hydrodynamic and thermal equations combined with upwind techniques for the convection terms and duality methods for nonlinear features are proposed.