Efficient and well-balanced numerical methods for nonhydrostatic three-dimensional shallow flows with moving beds and boundaries

许多沿海和河流问题，如水工建筑物周围的侵蚀，涉及陡坡、自由表面流动、移动边界、非静水压力、快速侵蚀/沉积，以及在某些情况下的超临界流。对此类问题进行高效、准确的仿真，可以极大地提高水利基础设施的设计、维护和管理水平。此外，随着计算系统和云计算设施的可用性和进步的增加，对特定于水文环境问题的改进计算方案有很大的需求，这些方案针对具有并行处理能力的计算机进行了优化，可以解决具有复杂流动状态和移动床和边界的问题。本研究计划的目的是提高三维非静压流动和移动床和边界的泥沙输移全耦合模拟的计算方案的准确性和性能。研究计划包括两个方面：发展增强的时间整合方案，以及发展专门为沿海和河流应用而设计的空间离散化方法，其中水平尺度通常大于垂直尺度。为此，将开发具有高精度和高效率的新型优化数值方案，特别强调大时间步长和大域的效率和稳定性，以及在具有并行处理能力的计算机上实现的能力。在这些方案中，泥沙输运方程和流动方程将以完全耦合的形式求解，模型将能够模拟复杂的流动形式，如混合亚/超/跨临界流动。所提出的数值模型的一个重要特征是能够执行耦合的2D/3D模拟，这将使其适用于广泛的工程问题，包括尖锐的表面梯度，快速侵蚀/沉积和移动边界。本研究提出的方法可以应用于许多实际问题，包括由强烈风暴潮或海啸引起的建筑物周围侵蚀引起的快速冲刷问题，山洪引起的桥墩周围冲刷问题，尾矿坝溃决等。其他应用包括早期预警系统和现场和实验室案例的实时模拟，其中模型的速度和效率起着至关重要的作用。此外，这些先进的建模工具可以帮助广泛的用户，包括设计师、数值建模者和风险管理应用中的决策者，以及水利基础设施的设计和维护，以应对极端降水、洪水和风暴潮强度的增加，这些通常会导致快速侵蚀和沉积。

Many coastal and riverine problems such as erosion around hydraulic structures involve sharp gradients, free-surface flows, moving boundaries, nonhydrostatic pressure, rapid erosion/sedimentation, and in some cases, supercritical flows. The efficient and accurate simulation of such problems can tremendously improve the design, maintenance, and management of hydraulic infrastructures. Furthermore, with the increasing availability and progress of computing systems and cloud computing facilities, there is a substantial need for improved computational schemes specific to hydro-environmental problems that are optimized for computers with parallel processing capability and can solve problems with complex flow regimes and moving beds and boundaries. The objective of this research program is to enhance the accuracy and performance of computational schemes for fully coupled simulation of 3D non-hydrostatic flow and sediment transport with moving beds and boundaries. The research program comprises two axes: the development of enhanced temporal integration schemes, and the development of spatial discretization methods specifically designed for coastal and riverine applications where the horizontal scales are typically larger than the vertical scales. To this end, novel optimized numerical schemes with high levels of accuracy and efficiency will be developed with particular emphasis on efficiency and stability for large time steps and large domains, as well as the capability of implementation on computers with parallel processing capacity. In these schemes, the sediment transport equations and the flow equations will be solved in a fully coupled form, and the model will be able to simulate complex flow regimes such as mixed sub/super/trans-critical flows. An important feature of the proposed numerical model is the ability to perform coupled 2D/3D simulations, which will make it applicable and efficient for a wide range of engineering problems involving sharp surface gradients, rapid erosion/sedimentation, and moving boundaries. The methodology proposed in this research can be applied in a number of practical problems, including fast-scour problems such as those induced by severe storm surges or tsunami-induced erosion around structures, scouring around bridge piers caused by flash floods, tailing-dam breaching, etc. Other applications include early warning systems and real-time simulations of field and lab cases where the speed and efficiency of the model plays a crucial role. Moreover, these advanced modeling tools can help a wide range of users, including designers, numerical modelers, and decision-makers in risk management applications and in the design and maintenance of hydraulic infrastructure in order to deal with the increased intensity of extreme precipitation, flooding, and storm surges, which typically lead to rapid erosion and sedimentation.