Jessica Padrone

The research activity deals with the development and of an innovative Lattice Boltzmann hydraulic model for shallow water flows. The shallow water equations (SWE) derived from depth-averaging Navier-Stokes equations. They allow simulating flows where the horizontal length scale is larger than the fluid depth. This assumption can introduce errors in describing the spatial and temporal distribution of the flow fields. On the other side, the model is also developed to investigate the simulation of flood events in urban areas. Even if there are already many numerical methods usually employed for these aims, the capture of 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.

The research aims are reproducing the dynamics of multilayer shallow water flows and modeling large-scale urban floods. Instead of use a full 3d model, the use of a multilayer model allow to have a description of the vertical variation of hydrodynamic quantities of large scale geophysical flows and the intrinsic simplicity of a Lattice Boltzmann model opens up the possibility of deepening the computational aspects of the density layered shallow water flows (e.g. gravity currents). The simulation of flood events is carried out introducing a new porosity approach, aimed at developing technical solutions for the assessment and mitigation of flood risk.

The model uses a multi relaxation time approach and a cascaded 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. The initial two layers model (CaLB-2), was extended to represent a n-layer flow (CaLB-N) and simulate free surface currents, where the 3D aspects are not negligible, introducing a formulation of the interchange forces between layers. For the large-scale urban inundation modelling, the introduction of a new porosity-based Lattice Boltzmann model is made considering the storage porosity in the SWE and introducing it in the source term of the Lattice Boltzmann model.

The validation phase is conducted considering experimental and numerical results available in literature, such as the classical Riemann problem, the case of a gravity current originating from two liquid layers and the case of an asymmetrical ideal dam break. The results obtained in reproducing the dynamics of shallow water flow are satisfactory and very promising for the new CaLB-N, demonstrating that the model is well established and ready for the most varied engineering applications. The introduction of new a porosity-based Lattice Boltzmann model is expected to allow capturing the effects imposed by structures and small-scale obstructions, providing an accurate representation of the source term to simulate realistic shallow water flows.