In this study, we propose a refined hydrodynamic lubrication model that incorporates a high-accuracy numerical algorithm for starved lubrication involving free surfaces. The performance of the proposed method is compared against that of the conventional model and numerical scheme. The results indicate that the Elrod-Adams model underestimates the hydrodynamic pressure due to unrealistic assumptions regarding the mass transport velocity of the lubricant beyond the contact region. Furthermore, the conventional numerical scheme fails to correctly predict the location of the rupture point and loses accuracy under conditions of severe starvation or high sliding speeds. In contrast, our proposed model ensures the conservation of mass flow between the outlet and inlet, while the new numerical algorithm restores the accuracy of the results.