Supposing the usage of a less viscous fluid to displace another more viscous, the unfavorable resulting mobility gradient triggers the development of viscous instabilities in the interface between both fluids, known as Saffman-Taylor Instabilities. This particular viscous instability has been the case study of several thesis and investigations throughout the last decades, especially because of the several applications of such phenomenon, casually known as viscous fingering, in industrial processes, most notably the second and third recovery of oil extraction. Historically, these investigations have been applying the Darcy s Law as the mathematical model for the flow dynamics. However, despite the fundamentally sound theory behind it, the averaging procedures of its development my hinder the assertiveness of the results of the simulation applied to flows in Hele-Shaw cells. Therefore, the investigations here conducted had their results based in the solving of the direct numerical simulations, or DNS, of the complete three dimensional Navier-Stokes equations coupled with equations of convection and diffuseness. Our objective is to study the linear and non-linear behavior of the viscous interface between fluids pairs that present non-monotonic behaviors. Besides the primary discrete modeling and numerical simulation, a particular emphasis is placed on the identification of influencing patterns of two governing parameters, the relative viscosity and Péclet number, on the change of behavior of the fluid flow. Simultaneously, optimization studies where conducted to identify the necessary resolution of the mesh discretization, in order to reduce the computational costs of further investigations. Through bi-dimensional simulations we were able to observe the development of quasi-steady state viscous interfaces in flows which featured sufficiently high viscosity ratios and Péclet numbers. Further investigations will be needed to study the propagation of the viscous fingers in the presence of flow disturbances, as also to disitnguish particularities of non-linear flows, in order to subsequently develop parametric solutions for the flow dynamics.