The aim of this paper is to present a three dimensional numerical model to compute incompressible fluid flows in thin lubricant films where inertia effects cannot be neglected. For this purpose, an averaged inertia method is used. A numerical scheme based on the finite element method is presented to solve simultaneously the momentum and continuity equations. The numerical model is then validated by confronting it with previously published analytical, experimental and numerical results. Particular attention is devoted to analysing the numerical conservation of mass and momentum. Moreover, the influence of mesh size on numerical precision is analysed. Finally, the model is applied to a misaligned hydrostatic seal. These seals operate with a substantial leakage flow, where non-laminar phenomena occur. The influence of inertia and misalignment of the faces on the seal behaviour is analysed through a comparison with an inertialess solution. Significant differences are observed for high values of the tilt angle when the flow is non laminar. Inertia effects in increased when the flow is laminar.

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