2D Shallow Water modelling of flood propagation: GPU parallelization, non-uniform grids, porosity, reverse flow routing

This thesis concerns different aspects of the numerical modelling of flood propagation, and it addresses both theoretical and practical issues in the framework of explicit finite volume schemes for the Shallow Water Equations (SWEs). The first part of the thesis is dedicated to investigate the capability of the GPU-parallelized numerical scheme developed at the Department of Engineering and Architecture of the University of Parma to produce real flood events. In particular, the flood occurred on the Secchia River in January 2014 is simulated on a domain of about 180 km2. The adoption of a Cartesian grid of approximately 7.2 M cells (with size 5 m) allows the description of all major embankments that potentially influence the flood evolution inside and outside the river region. The numerical scheme is modified to simulate levee breaches, and the results are validated against aerial and satellite images. Despite the high-resolution adopted, the GPU parallelization guarantees a ratio of simulation to physical times of about 1/15 (about 6 computing hours are necessary to simulate 90 h of physical time). The simulation of this real flood highlights that the major limitation of the existing numerical scheme is the use of uniform Cartesian grids, which unavoidably limit the maximum size of the domain, and/or prevent the adoption of zones with different resolution. Therefore, this limitation is addressed by implementing a novel grid type named Block Uniform Quadtree that introduces non-uniform grids, while allowing exploiting GPU capability. Theoretical and laboratory tests demonstrate that speed-ups of up to one order of magnitude can be achieved (with comparable level of accuracy) in comparison with uniform Cartesian grids. The capability of the model of simulating large domains is demonstrated by performing a hypothetical flood event induced by a levee breach in a real 83 km-long river reach, considering a domain of 840 km2, with maximum resolution of 5 m. In this simulation, a ratio of physical to computational time of about 12 is obtained. Another critical aspect of flood simulation is the representation of urban areas. Despite the efficiency of the numerical scheme, the description of buildings and streets in the computational mesh requires high-resolution elements (with size less than 1 m), and thus the simulation of large domains becomes impossible or extremely computationally expensive. To overcome this issue, sub-grid models based on porosity are investigated and implemented in the numerical scheme. In particular, two different SWE formulations based on porosity are analyzed. The first one is obtained by adding a source term and preserving the computational scheme of a classical SWE solver, which inherently guarantees the C-property. In a second formulation, a novel augmented Riemann Solver capable of handling porosity discontinuities in 1D and 2D SWE models is derived, and its capability of capturing different wave patterns is assessed against several Riemann Problems with different wave patterns. After having implemented and validated a stable, accurate and fast numerical model for the solution of the 2D-SWEs, in the last part of the thesis, the model is used in the framework of a Bayesian methodology for solving inverse problems: the goal is the estimation of an unknown inflow hydrograph in an ungauged river section. The inverse procedure is parallelized as to take advantage of High Performance Computing clusters with GPUs, and the procedure is validated considering real river reaches and different flood wave shapes. The parallel procedure reduces the computational times of about 8 times if compared to a serial procedure.