The subject of the present thesis is the development of a numerical solver to
study the violent interaction of marine flows with rigid structures.
Among the many numerical models available, the Smoothed Particle
Hydrodynamics (SPH) has been chosen as it proved
appropriate in dealing with violent free-surface flows. Due to its
Lagrangian and meshless character it can naturally handle breaking waves and
fragmentation that generally are not easily treated by standard methods. On
the other hand, some consolidated features of mesh-based methods, such as
the solid boundary treatment, still remain unsolved issues in the SPH
context.
In the present work a great part of the research activity has been devoted
to tackle some of the bottlenecks of the method. Firstly, an enhanced SPH
model, called delta-SPH, has been proposed. In this model, a proper numerical diffusive
term has been added in the continuity equation in order to remove the spurious
numerical noise in the pressure field which typically affects the weakly-compressible SPH
models. Then, particular attention has been paid to the development of suitable
techniques for the enforcement of the boundary conditions. As for the free-surface, a
specific algorithm has been designed to detect free-surface particles and
to define a related level-set function with two main targets: to allow the
imposition of peculiar conditions on the free-surface and to analyse and
visualize more easily the simulation outcome (especially in 3D cases).
Concerning the solid boundary treatment, much effort has been spent to
devise new techniques for handling generic body geometries with an adequate
accuracy in both 2D and 3D problems. Two different techniques have been
described: in the first one the standard ghost fluid method has been
extended in order to treat complex solid geometries. Both free-slip and
no-slip boundary conditions have been implemented, the latter being a quite
complex matter in the SPH context. The proposed boundary treatment proved
to be robust and accurate in evaluating local and global loads, though it
is not easy to extend to generic 3D surfaces.
The second technique has been adopted for these cases.
Such a technique has been developed in the context of Riemann-SPH methods
and in the present work is reformulated in the context of the standard SPH scheme.
The method proved to be robust in treating complex 3D
solid surfaces though less accurate than the former.
Finally, an algorithm to correctly initialize the SPH simulation in the case of generic
geometries has been described. It forces a resettlement of the fluid particles
to achieve a regular and uniform spacing even in complex configurations. This
pre-processing procedure avoids the generation of spurious currents due to
local defects in the particle distribution at the beginning of the simulation.
The delta-SPH model has been validated against several problems
concerning fluid-structure interactions. Firstly, the capability of the
solver in dealing with water impacts has been tested by simulating a
jet impinging on a flat plate and a dam-break flow against a vertical
wall. In this cases, the accuracy in the prediction of local loads and of
the pressure field have been the main focus. Then, the viscous flow around
a cylinder, in both steady and unsteady conditions, has been simulated
comparing the results with reference solutions. Finally, the generation
and propagation of 2D gravity waves has been simulated. Several
regimes of propagation have been tested and the results
compared against a potential flow solver.
The developed numerical solver has been applied to several cases of
free-surface flows striking rigid structures and to the problem of the
generation and evolution of ship generated waves. In the former case, the
robustness of the solver has been challenged by simulating 2D and 3D water impacts
against complex solid surfaces. The numerical outcome have been compared
with analytical solutions, experimental data and other numerical results
and the limits of the model have been discussed.
As for the ship generated waves, the problem has been firstly studied
within the 2D+t approximation, focusing
on the occurrence and features of the breaking bow waves. Then, a
dedicated 3D SPH parallel solver has been developed to tackle the simulation
of the entire ship in constant forward motion. This simulation is quite demanding in
terms of complexities of the boundary geometry and computational resources
required. The wave pattern obtained has been compared against experimental
data and results from other numerical methods, showing in both the cases a fair
and promising agreement