Immersed boundary method for cavitating and biological flows

The aim of the present work is the development of a computational tool to ease the numerical simulation of cavitating flows in domains of complex topology or with arbitrary moving boundaries. Within the framework of Computational Fluid Dynamics(CFD), an Immersed Boundary (IB) Method has been developed. According to the IB methodology, the grid that discretises the computational domain does not need to conform to the geometry and the solid boundaries are modelled on a fixed canonical grid by alternations of the governing equations in their vicinity. This modelling strategy is beneficial in terms of both computational cost and numerical solution. The grid generation, which is a complex and time consuming process, is simplified as a regular canonical grid, non-conformal to the boundaries, can be used. In addition, when moving boundaries are present, a conformal grid would need to adapt or deform following the motion of boundaries, which would increase the computational cost of the simulations in the first case and affect the solution in the latter case; the use of IB method alleviates these issues. The developed method follows the direct-forcing approach, which simply adds to the governing equations a source term to account for the body force acting on the fluid. The simplicity of the method makes it suitable for complex flow regimes, including phase change, strong shocks and compressibility effects, as well as Fluid Structure Interaction (FSI). Since cavitation dynamics regard a wide range of applications of engineering interest, from hydraulic machines to novel therapeutic techniques, the method is designed to be applicable in a wide range of flow regimes. Turbulent modelling and flow induced motion has been taken into account. The method has been successfully applied to cavitating and incompressible cases where conventional techniques are not easily or at all applicable. The shock-wave interaction with material interfaces is studied via the high-speed impact of a solid projectile on a water jet, which has been studied only experimentally before and only qualitative observations existed. The numerical investigation with the proposed methodology unveiled rich information regarding the physics of the impact, the resulting shock formation, cavitation development and interface instabilities initiation. Moreover, the methodology was applied on the thoroughly studied pulsatile flow through a bi leaflet Mechanical Heart Valve, to provide additional information regarding shear stress development. The methodology aids an experimental campaign employing novel shear stress measuring techniques, carried out by our collaborators. The research work and the developed method described in the present Thesis, intend to set the foundations for more elaborate numerical investigations of highly complex problems of Fluid Dynamics.