Modelling Fluid Structure Interaction problems using Boundary Element Method

This dissertation investigates the application of Boundary Element Methods (BEM) to Fluid Structure Interaction (FSI) problems under three main different perspectives. This work is divided in three main parts: i) the derivation of BEM for the Laplace equation and its application to analyze ship-wave interaction problems, ii) the imple- mentation of efficient and parallel BEM solvers addressing the newest challenges of High Performance Computing, iii) the developing of a BEM for the Stokes system and its application to study micro-swimmers.First we develop a BEM for the Laplace equation and we apply it to predict ship-wave interactions making use of an innovative coupling with Finite Element Method stabilization techniques. As well known, the wave pattern around a body depends on the Froude number associated to the flow. Thus, we throughly investigate the robustness and accuracy of the developed methodology assessing the solution dependence on such parameter. To improve the performance and tackle problems with higher number of unknowns, the BEM developed for the Laplace equation is parallelized using OpenSOURCE tech- nique in a hybrid distributed-shared memory environment. We perform several tests to demonstrate both the accuracy and the performance of the parallel BEM developed. In addition, we explore two different possibilities to reduce the overall computational cost from O(N2) to O(N). Firstly we couple the library with a Fast Multiple Method that allows us to reach for higher order of complexity and efficiency. Then we perform a preliminary study on the implementation of a parallel Non Uniform Fast Fourier Transform to be coupled with the newly developed algorithm Sparse Cardinal Sine De- composition (SCSD).Finally we consider the application of the BEM framework to a different kind of FSI problem represented by the Stokes flow of a liquid medium surrounding swimming micro-organisms. We maintain the parallel structure derived for the Laplace equation even in the Stokes setting. Our implementation is able to simulate both prokaryotic and eukaryotic organisms, matching literature and experimental benchmarks. We finally present a deep analysis of the importance of hydrodynamic interactions between the different parts of micro-swimmers in the prevision of optimal swimming conditions, focusing our attention on the study of flagellated “robotic” composite swimmers.