A cell-vertex finite volume method for thermohydrodynamic problems in lubrication theory

In this work a coupled model in pressure and temperature is proposed and numerically solved for lubrication problems in journal-bearing devices. More precisely, a non-linear free boundary elliptic problem for the hydrodynamic behaviour, including cavitation phenomena, and a convection–diffusion problem with non-linear source due to viscous dissipation for the thermal aspects. The numerical method to calculate the pressure involves finite element approximations jointly with upwind techniques for convection and duality algorithms for non-linearities. But the main innovative goal concerns with the temperature computation by introducing a second-order cell-vertex finite volume scheme as an alternative strategy to classical first-order finite element or finite volume approximations.