Finite Element simulations: computations and applications to aerodynamics and biomedicine

Sammanfattning:   Partial Differential Equations describe a large number of phenomena of practical interest and their solution usually requires running huge simulations on supercomputing clusters.  Especially when dealing with turbulent flows, the cost of such simulations, if approached naively, makes them unfeasible, requiring modelling intervention.  This work is concerned with two main aspects in the field of Computational Sciences.  On the one hand we explore new directions in turbulence modelling and simulation of turbulent flows; we use an adaptive Finite Element Method and an \emph{infinite Reynolds number} model to reduce the computational cost of otherwise intractable simulations, showing that we are able to perform time-dependent computations of turbulent flows at very high Reynolds numbers, considered the main challenge in modern aerodynamics.  The other focus of this work is on biomedical applications.  We develop a computational model for (Cardiac) Radiofrequency Ablation, a popular clinical procedure administered to treat a variety of conditions, including arrhythmia.  Our model improves on the state of the art in several ways, most notably addressing the critical issue of accurately approximating the geometry of the configuration, which proves indispensable to correctly reproduce the physics of the phenomenon.