Sviluppo di un modello idraulico di Boltzmann a reticolo multistrato e basato sulla porosità per flussi di acque poco profonde

In this thesis, the development of an innovative Lattice Boltzmann hy draulic model for shallow water flows is presented. The model uses a multi relaxation time (MRT) approach and a cascaded and cumu lant collision operator based on central moments, different from the standard BGK approach with single relaxation time, with the aim of increasing the number of adjustable parameters and improve stability and accuracy. Since the stability range is similar, the collision opera tor (cascaded or cumulant) that offers the best accuracy and stability in the simulations is chosen on an as-needed basis. The thesis focuses on two main purposes: reproducing the dynamics of multilayer shallow water flows and modeling large-scale urban floods. The use a multilayer cascaded collision operator-based model allows obtaining a description of the vertical variation of hydrodynamic quantities of large-scale geo physical flows and deepening the computational aspects of the density layered shallow water flows. The two liquid-layer initial model (CaLB 2) has been then extended to simulate the dynamics of n-layer shallow water flows (CaLB-N). The model solves the shallow water equations by considering several sets of particle distribution functions (PDFs), one for each layer, that are solved separately. Layers are connected by coupling terms, defined as external forces that model the mutual actions between the layers, whose mathematical formulation is obtained experimentally. The simulation of flood events in large urban areas is also investigated, using the cumulant collision operator based model (CLB). Although there are already many numerical methods (finite difference, finite vol ume and finite element methods), usually employed for these aims, cap turing localized flow features in large scale is still a challenge, due to the size of urban areas and the vastly different spatial scales involved in inundation processes, exacerbated by bed slope and friction forces. The introduction of a new porosity-based Lattice Boltzmann model (CLB-P) 4 makes possible to capture the effects imposed by structures and small scale obstructions, providing an accurate representation of the source term to simulate realistic shallow water flows, with a reduced compu tational cost. The model is validated through comparisons with ex perimental and numerical results from test cases available in literature and through the modeling of a real flood event; the applicability of the suggested mathematical model for hydraulic engineering applications is explored, paving the way for new approaches and improvements, to have a realistic modeling of shallow water flows