Local-inertial shallow water model on unstructured triangular grids

Abstract

Abstract Two-dimensional shallow water models are widely used for flood risk assessment. Application of these models to large-scale urban areas significantly increases the computational cost as it requires high-resolution simulations to capture the complex hydrodynamic processes. Hence, simplified models that are based on local-inertial formulations have been proposed by different researchers. Although these models are successful in simulating floods, their applications are limited by the use of structured grids and instability issues. Structured grids do not have the flexibility of providing different mesh resolutions to model the computational domain. Importantly, in the case of structured grids, the use of a single grid or the combination of finer and coarser grids inevitably increases the overall computational time. To overcome all these problems, an unstructured grid-based local-inertial model is developed. The performance of the model is rigorously evaluated by solving analytical test cases and simulating an urban flood in Glasgow, UK. Finally, the model is applied to simulate a catastrophic flood event that occurred in Chennai, India. The simulated water depths and inundation extents are compared with observed data or full-2D model results. The investigations show that the developed model has the potential for simulating floods on a large-scale with high-resolution grids at a comparatively lower computational cost than its predecessors for a similar range of accuracy. Flooding is one of the natural hazards that pose a great threat to life and property. Over the period 1980-2013, flooding has resulted in losses exceeding $1 trillion globally with more than 220,000 fatalities (Munich Re, 2014). The magnitude and frequency of floods are increasing due to the combined effect of rapid urbanization and climate change, especially in urban areas (Wasko and Sharma, 2017). As a consequence, low-lying urban areas have become more susceptible to flooding. Therefore, assessment of flood risk is crucial in the development of flood management strategies that help in mitigating the resultant economic and social impacts. In order to forecast and evaluate flood risk, numerical models are being used extensively. However, these models cannot produce accurate results or may not be computationally efficient enough for forecasting floods with a reasonable lead time for emergency action if they are unable to handle fine topographical details. Two-dimensional (2D) models that solve the depth-averaged shallow water equations (SWEs) have been at the forefront of flood modelling because of their ability to capture the spatial variability of floodplain hydraulics utilizing high-resolution topography while employing robust numerical methods. Therefore, it is not surprising that substantial research has been devoted to the development of 2D models using various numerical methods over the years (Peraire et al., 1986; Bermudez et al., 1991; Hubbard, 1999; Sanders et al., 2008; Liang, 2010; Cea and Blade, 2015). The high-resolution simulations handling a detailed representation of topographical features are essential in urban areas to better capture the complex hydrodynamic processes through the maze of built infrastructure (Horritt and Bates, 2001; Brown et al., 2007; Fewtrell et al., 2008; Neal et al., 2009; Horritt et al., 2010; Sampson et al., 2012). Despite the explosion of computational power and substantial progress in numerical methods, the application of 2D models to large domain with high spatial resolution, especially for issuing early warnings, still demands high computational cost (Marks and Bates, 2000; de Almeida et al., 2012). To improve the computational efficiency, four different approaches are currently adopted: (i) high-performance computing architectures taking advantages of GPGPU (Kalyanapu et al., 2011), distributed memory parallelization (Pau and Sanders, 2006, Neal et al., 2009), multi-core central processing units (MCs) and cloud computing (Lamb et al., 2009); (ii) a simplified hydraulic model approach that uses the simplified formulations of SWEs, for example, local-inertial LISFLOOD-FP (Bates et al., 2010) and Quasi 2D (Kuiry et al., 2010) models; (iii) a coarse-grid approach, in this case computational time is reduced by either coarsening the grid size or using techniques like sub-grid treatment (Yu and Lane, 2011) and the porosity parameter (Sanders et al., 2008; Bruwier et al., 2017) and (iv) the Cellular Automata (CA) approach (Dottori and Todini, 2010; Guidolin et al., 2016), in which the use of a transition rule for spatial discretization improves the computation time. This study focuses on the simplified hydraulic model approach, which can also take some advantages like GPGPU, parallelization and sub-grid techniques to further reduce the computation time.