Since there has been an important increase in unmanned vehicles systems research such as quadrotors, a mathematical model and PID control laws are studied. Based on some dynamic variables, PID control is applied to compute a controller to be then use in autopilot simulations. As this kind of VTOL vehicle seems to be unstable, the aim of this work is to change even other flight mechanics parameters and control gains to study attitude and altitude variations. A well-known computational tool is used for simulation purposes, performance analysis and validation.

Motivated by the important growth of VTOL vehicles research such as quadrotors and to a small extent autonomous flight, a quadrotor dynamical model is presented in this work. The purpose of this study is to get a better understanding of its flight dynamics. It is an underactuated system. So, a simplified and clear model is needed to implement controllers on these kind of unmanned aerial systems. In addition, a computational tool is used for validation purposes. For future works embedded or intelligent control systems can be developed to control them. Gyroscopic and some aerodynamics effects are neglected.

The finite volume method have been developed to solve the Navier-Stokes equations with primitive variables and non dimensional form. This work examine the classical benchmark problem of the lid-driven cavity at a different Reynolds range (Re = 10,100,400, 1000, 2000, 3200) and several cavity geometries. The cavity configurations include square cavity, skewed cavity, trapezoidal cavity and arcshaped cavity. The flow is assumed laminar and solved in a uniform mesh. A CFD tool with its solvers (icoFoam) will be used for this study.

The chapter was inadvertently published with an incorrect version of an author's affiliation as "Universidad Manuel Beltrán" whereas it should correctly read "Universidad Manuela Beltrán".