The aim of this project has been to consolidate and amplify the knowledge on fluid dynamics and CFD. It will be developed and verified different numerical codes for each physical case (potential flow, convection-diffusion equation and Navier-Stokes equation).The first chapter will consist on an introduction, where it will be explained the aimand the requirements of this study, a background of numerical methods, the reportor ganisation and it will be also mentioned the previous knowledge on numerical methods.On the following three chapters it will be solved and analysed three different cases of numerical approaches to fluid mechanics (non-viscid flows, convection-diffusionequations and, finally, the incompressible flow of Navier-Stokes equations). In each chapter it will be an introduction, a problem definition, a methodology of resolution (where it will be explained the procedure and the algorithm of the code), an analysis ofthe results (numerical and physical results) and finally a conclusion.On the fifth chapter it will be presented the budget, the task planning and the environmental impact and on the sixth chapter will consist on a conclusion and recommendations for a future work.