The large topological changes in the liquid-gas interface associated with various industrial applications, e.g. jet formation in inkjet printing process, necessitates acquiring special treatments in the numerical modelings using the level-set method. In spite of its overall efficiency and robustness, the well-known shortcoming of the level-set method is associated with the lack of a systematic approach to preserving the regularity of the distance (level-set) function. The regularity of the level-set function is lost mainly due to the stretching (or compressing) effect of the strain-rate, especially in the vicinity of the liquid-gas interface. The larger the deformation of the interface, the more severe the issue becomes. Frequent level-set reinitialization is conventionally adopted as an effective treatment for this issue. However, the traditional approach based on the hyperbolic Hamilton-Jacobi equation is a computationally expensive procedure. More importantly, stemming from the hyperbolicity of the formulation, the accuracy of the result strongly relies on the ad-hoc treatment of the blind spots in the vicinity of the liquid-gas interface cut by a substrate [1]. On the other hand, the present work relies on an elliptic level-set reinitialization approach that is not only more efficient but also benefits from an optimization step [2] that minimizes the reliance on the treatment of the blind spots. In this work the performance of the proposed approach is investigated.