Sviluppo di uno strumento di calcolo tridimensionale per l'analisi delle grandi deformazioni di fluidi e solidi viscosi

The primary purpose of this master thesis is to develop an efficient and robust Lagrangian Finite Element Method for the analysis of incompressible flows. The adapted formulation is based on the Particle Finite Element Method, that is a powerful tool for resolution of fluid-dynamics problems, including free-surface flow and breaking waves. An existing code, developed at the Department of Structural Engineering of the Politecnico di Milano, has been used as starting point for the implementation. First of all, the code is analyzed to reduce the computing time and subsequently the program Tetgen is introduced for the continuous re-triangulation of the domain. Special attention is devoted to the mass conservation problem with a detailed study of different formulations of the Fractional Step Method. The model is applied to sloshing problems and to simulate the mass propagation on a complex topography. This work is part of a research activity, currently in progress at the Department of Structural Engineering, aimed to develop a 3D model for the simulation of fluid-structure interaction problems and of landslide runouts.