Despite the intensive efforts to develop increased computational capabilities, mix models remain the most viable approach for the solution of many applications. These are an approximation to the true solution of the Navier-Stokes equations. The reason for this state of affairs becomes abundantly clear when one considers the difficulties of achieving the desired turnaround time for applied fluid dynamics calculations. In this chapter, we focus on some of the methodologies currently utilized to tackle the practical problem of simulating hydrodynamic instabilities in engineering designs.