A 2D smoothed particle hydrodynamics model for free surface applications - Πουλιάσης, Γεώργιος (Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Πολιτικών Μηχανικών. Τομέας Υδατικών Πόρων και Περιβάλλοντος, 2017)
Currently numerical simulations have become one of the approaches to tackle engineering and scientific problems. They are used in almost every discipline of science and engineering such us solid mechanics, fluid mechanics, climatic models etc. In addition the rapid development of computers, it has enabled the use of complicated numerical tools in professional engineering offices. Most methods are based on grids or meshes such as finite element method (FEM), finite difference method (FDM) and finite volume method (FVM). Particularly the latter is widely applied in computational fluid mechanics packages. However application of these methods, when considering problems with large deformations such as fracture, moving boundary, free surface flows and multiphase flows, has shown difficulties inherited from their grid nature. Because the entire formulation is based on the grid/mesh, a time‐consuming and costly process of generating/regenerating a quality grid/mesh is necessary. Moreover these grids/meshes in many cases need to vary in space and to time, thus inserting high complexities on the algorithm, consisting the development of one a formidable task. In order to tackle these problems researchers have focused on the development of mesh‐free methods. Smoothed Particle Hydrodynamics (SPH) is the most widely established method and has been applied in various fields of science and engineering such us astrophysics, computational solid mechanics, computational fluid dynamics, etc. Despite this method possesses serious advantages and strong conservation properties, a full consensus on its formulation has not yet been reached. Moreover, to the extent of the author’s knowledge there has not been a thorough investigation of the key aspects of classical SPH formulation. The purpose of this thesis is to develop a computer code based on the SPH method and conduct a thorough investigation of the response of this method to the change of various parameters of the method and numerical techniques. The thesis is structured as follows. First a brief presentation of the fundamental descriptions of fluids is given. Then the theoretical foundations of the SPH are analyzed and the basic equations comprising the method are derived. Subsequently the basic numerical components, such as boundary representation techniques and time integration schemes, are presented and discussed. Then the steps of the development of an algorithm are laid and the applications are presented. In order to check the validity of our code we have employed a classic benchmark case for the SPH, the collapse of a water column over a dry bed. After the validation we have conducted a thorough investigation on the behavior and performance of the method comprising of thirteen different parameter formulations over the same test case. In addition we have laid the foundations of imposing hydrostatic pressure as initial condition. Finally the results are discussed and conclusions are drawn as optimal guidelines for the use of the method, and suggestions for further improvements of the method and future work.