An active‐set mixed finite element solver for a transient hydrodynamic lubrication problem in the presence of cavitation

Abstract

In this paper, we study a moving free boundary problem related to the cavitation modeling in lubricated devices. More precisely, a characteristics method combined with a weak formulation in a mixed form is introduced for the Elrod‐Adams model. The formulation is suitable for the use of mixed finite element methods in the numerical approximation. It is proved that the time‐discrete problem and its finite element discretization have unique solutions. Further an efficient primal‐dual active‐set strategy is proposed to solve the resulting algebraic system. The performance of the overall algorithm is illustrated by numerical examples.

FELINE: Finite element solver for hydrodynamic lubrication problems using the inexact Newton method

“…The following solutions were obtained in a 200 × 200 element mesh, with 2D and sliced pressure and cavitation profiles for problem 1 shown in figures 3 and 4. Our results are in excellent agreement with profiles of references [13] and [19]. The 2D and sliced results for problem 2 and 3 are shown in figures (5,6) and (7,8) respectively, closely matching the 1D profiles of [13].…”