Two-dimensional and three-dimensional non hydrostatic models for fully non-linear and dispersive hydrodynamic processes

The thesis is divided in two main parts. In the first part is presented a model based on a numerical integration of a new conservative form of the Fully Non-linear Boussinesq Equations (FNBE) in a contravariant formulation. As known coastal regions are characterized by a very complex morphology: presence of anthropic structures, river mouth or shoreline with articulated geometry. The use of orthogonal grid, as Cartesian coordinate, requests a huge number of calculus points that may be prohibitive. To solve this issue, a well known strategy is to integrate the motion equations on generalized curvilinear boundary conforming grid. In the second part it is presented an original fully non-hydrostatic three-dimensional model based on the numerical integration of Navier-Stokes Equations in time dependent coordinate system. The use of time dependent coordinate system allows to assign, without any approximations, bottom and free surface kinematic conditions and zero pressure condition at the upper boundary of the domain. Unlike the depth averaged model, this model is able to simulate the three-dimensionality of hydrodynamic phenomena related to the wave motion of unsteady flows. The proposed model belongs to the group of the so-called “free surface fully non-hydrostatic three-dimensional models”. These models are often used to analyze local phenomena, to evaluate flow-structure interaction, for sediment transport analysis and to study turbulences phenomena related with them. In general the free surface fully non-hydrostatic three-dimensional models are used for all engineering problems for which is necessary to know the vertical distribution of hydrodynamic quantities.