Towards the application of the isogeometric boundary element analysis to fluid mechanics: non-linear gravity waves and dynamics of deformable capsules in shear flows

Identifier:  TDX:2501

Handle: https://hdl.handle.net/20.500.11797/TDX2501

Authors:  Maestre Heredia, Jorge

Abstract:
In this Thesis an efficient and robust numerical model for the analysis of fluid dynamic problems has been developed, validated and applied to two novel fluid flow configurations: (1) the waves generated by a submerged foil and (2) the dynamics of microcapsules in pulsating shear flows. The model is based on the Boundary Element Method (BEM) integrated with the NURBS and the T-spline frameworks. This technique is known as Isogeometrical Analysis (IGA) and it offers several advantages. The most attractive is that it allows a direct integration between modern Computer Aid Design geometric systems and numerical engineering analysis tools, removing intermediate steps as the mesh generation. This Thesis is divided into two blocks. The first block deals with the simulation of the propagation of non-linear gravity waves and of the wave-structure interactions. The analysis of this phenomenon is useful to predict the generation and propagation of tsunamis and it is indispensable for the design of breakwaters and floating structures. The flow is assumed to be inviscid and irrotational and the resulting Laplace's equation is solved using BEM. Some benchmark examples are considered to show the temporal accuracy and stability of the method. In addition, the simulation of the waves generated by submerged foils is reported. In the second block the IGA is applied to analyze the behavior of deformable microcapsules in shear flows. The dynamics of deformable capsules have important implications in a wide range of biolomedical and industrial applications. The IGA-BEM is used to solve the Stokes flow equation and an IGA-Finite Element Method (FEM) is developed for the analysis of the capsule mechanics. Some benchmark examples are solved to demonstrate the capability of the present approach for the simulation of capsules subjected to large deformation. Finally, the dynamics of a deformable capsule in a tube under a pulsatile flow is analyzed.