Abstract: Nowadays, the fields where computational fluid dynamic is being applied are growing in number and importance very fast. Just to mention few applications, from aerospace to automotive ones, from architectural to environmental ones and only most recently medical ones to optimize some surgical interventions about cardiovascular or breathing apparatus. On the other hand, unfortunately, obtaining some useful results by solving fluid dynamic equations over complex domains, can be very difficult because of the processing power needed or computational time machine requested. This is why

during the last years it has been worked a lot in order to develop several new techniques able to solve this kind of problems in an easier way by accomplishing two goals: reduction of computational time needed and increment of the solution accuracy without augmenting the CPU power. In this work we would like to compare some of these techniques (RB, POD, HiMOD, HiPOD, HiRB) by the use of the finite element library FEniCS with a Python interface.