Two-dimensional discontinuous Galerkin shallow water model for practical flood modelling applications

Finite volume (FV) numerical solvers to the two-dimensional shallow water equations are the foundation of the current state-of-the-practice, industry-standard flood models. The second-order Discontinuous Galerkin (DG2) alternative show a promising way to improve current FV-based flood model formulations, but is yet under-studied and rarely utilised to support flood modelling applications. This is contributed by the mathematical complexity constructed within the DG2 formulation that could lead to large computational costs and compromise its stability and robustness when used for practical modelling. Therefore, this PhD research aims to develop a new flood model based on simplified DG2 solver that is improved for flood modelling practices. To achieve this aim, three objectives have been formed and addressed through analyses involving academic and experimental test cases, as well as test cases that are recommended by the UK Environment Agency to validate 2D flood model capabilities, whilst benchmarking the simplified DG2 solver against four FV-based industrial models. Key research findings indicate that the simplified DG2 solver can equally retain conservative properties and provide second-order accurate predictions as the standard DG2 solver whilst offering around 2.6 times runtime speed up. Additionally, the simplified DG2 solver can be reliably efficient to provide predictions close to the outputs of the industrial models, in simulating flood scenarios covering large catchment-scale areas and at a grid resolution greater or equal than 5 m, particularly when the local limiting is disabled. However, the local limiting is still needed by the simplified DG2 solver when modelling detailed velocity fields at sub-metre grid resolutions, particularly in regions of highly active wave-structure interactions as commonly encountered in urban flooding around steep-sloped building structures.