Efficient large-scale real-world flood simulations using the shallow water equations on GPUs

Abstract

Climate change is one of the largest challenges humanity has to cope with today. Earth-orbiting satellites and other technological advances have enabled scientists to see the big picture, collecting many different types of information about our planet and its climate on a global scale. Data collected over many years reveals the signals of a changing climate. Europe and the northern hemisphere are warming at faster pace than the global average. Europe's Atlantic-facing countries are predicted to suffer heavier rainfalls, greater flood risk, more severe storm damage, according to the most comprehensive study of Europe's vulnerability to climate change. National Aeronautics and Space Administration (NASA) and National Oceanic and Atmospheric Administration (NOAA) confirmed that 2016 had broken the record for the hottest year ever previously held by 2015, which had itself broken the record that had been held by 2014. According to a climate change report from 2014, global sea level rose about 20 centimetres in the last century. The rate in the last two decades, however, is nearly double that of the last century. Moreover, in the last years a surprisingly large number of major floods happened around the world, which suggests that floods may have increased and will continue to increase in the near future. Modern science in combination with the latest simulation technologies can help to understand the cause and the impact of the adverse phenomena related to climate change. Moreover, we can exploit our knowledge and simulation tools to prepare response measures which aim at reducing the risk associated with flood events. Today, a lot of effort is put into making flood simulations faster and more accurate to increase both computational efficiency and fidelity of the results. The aim of this thesis is to provide an efficient and robust simulation tool for large-scale flood simulations that can be used to support decision making. This goal is addressed by developing a new scheme for the shallow water equations (SWE), implementing it efficiently for graphics processing units (GPUs) and validating it on analytic, laboratory and real-world cases in comparison with other schemes. Chapter I starts with a motivation for this thesis. This is followed by a general overview on fluid and flood simulations including the introduction of the SWE along with discretization methods for them. The next section gives a short insight into GPUs architectures and justifies the suitability of the SWE for parallel computations on these devices. In the last section of the chapter the main goals of this thesis are explained. In Chapter II, we propose a new two-dimensional numerical scheme named HWP, to solve the SWE. The HWP scheme is an enhanced version of a scheme by Kurganov and Petrova (KP), which aims to improve the solution in the presence of partially flooded cells. The presented scheme is well-balanced, positivity preserving, and handles dry states. Mass conservation is ensured by using the draining time step (DTS) technique in the time integration process, which guarantees non-negative water depths. Unlike the KP scheme, our technique does not generate high velocities at the dry/wet boundaries, which are responsible for small time step sizes and slow simulation runs. We prove that the new scheme preserves ¿lake at rest' steady states and guarantees the positivity of the computed fluid depth in the partially flooded cells. We compare the new scheme, along with the KP scheme, against the analytical solution for a parabolic basin and show the improved simulation performance of the new scheme for two real-world scenarios. Chapter III presents a new GPU implementation for the HWP and KP schemes on Cartesian grids. Previous implementations are not fast enough to evaluate multiple scenarios for a robust, uncertainty-aware decision support. To tackle this, we exploit the capabilities of the NVIDIA Kepler architecture and the new shuffle instructions. The KP scheme is simpler but suffers from incorrect high velocities along the wet/dry boundaries, resulting in small time steps and long simulation run-times. The HWP scheme resolves this problem but comprises a more complex algorithm, that represents an extra burden on the GPU. Here, an efficient and novel shuffle-based implementation is presented for both schemes. Moreover, a performance comparison is provided, in which we compare shuffle-based implementations with pure shared memory versions. The correctness and performance is validated on real-world scenarios. In Chapter IV an exhaustive comparison and validation is performed and presented, which contains important use cases essential for developers and practitioners working with flood simulation tools. We discuss three state-of-the-art shallow water schemes, one by Kurganov and Petrova (KP), its successor by Horváth et al. (HWP), and our two-dimensional extension of the scheme by Chen and Noelle (CN). We analyse the advantages and disadvantages of each scheme on an extensive list of scenarios including several analytical and laboratory cases as well as a representative set of three historical floods. To enable the real-world studies, we address the implementation of the required boundary conditions (BCs), such as wall BCs, discharge BCs and water level BCs. Chapter V contains a summary and the findings presented in this thesis, which advance the knowledge in simulating floods using the SWE on GPUs. The new HWP scheme tackles the non-physical velocities that appear along the dry/wet boundaries. This not only improves the numerical accuracy, but allows for faster simulation since there are no high velocity spots that act as a limiting factor on the time step sizes. Furthermore, an efficient GPU implementation is presented with focus on the reduction of the computational burden introduced by the HWP scheme. Finally, the validation cases give a comprehensive overview of three SWE schemes and reveal their strengths and weaknesses under various conditions. We observe that the KP and HWP schemes are more accurate than the CN scheme in some cases, however, in other cases they suffer from non-physical oscillations. Overall, good agreement is observed for all case studies rendering the presented shallow water schemes suitable for flood management applications.