Mathematics

Nowadays, the fields where computational fluid dynamic is being applied are growingin number and importance very fast. Just to mention few applications, fromaerospace to automotive ones, from architectural to environmental ones and onlymost recently medical ones to optimize some surgical interventions about cardio-vascular or breathing apparatus.On the other hand, unfortunately, obtaining some useful results by solving fluiddynamic equations over complex domains, can be very difficult because of theprocessing power needed or computational time machine requested. This is whyduring the last years it has been worked a lot in order to develop several newtechniques able to solve this kind of problems in an easier way by accomplishingtwo goals: reduction of computational time needed and increment of the solutionaccuracy 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 thefinite element library FEniCS with a Python interface.  Joint work between SISSA mathLab and MOX-Politecnico di Milano.