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

具有移动床和边界的非静水三维浅流的高效且平衡的数值方法

• 批准号: RGPIN-2020-06278
• 负责人: Mohammadian, Abdolmajid
• 金额: $ 4.29万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=741133
• 关键词: Efficient; well; balanced; numerical; methods

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.

许多沿海和河流问题，例如水工结构周围的侵蚀，涉及陡峭的梯度、自由表面流、移动边界、非静水压力、快速侵蚀/沉积，在某些情况下还涉及超临界流。对此类问题进行高效、准确的模拟可以极大地改善水利基础设施的设计、维护和管理。此外，随着计算系统和云计算设施的可用性和进步，迫切需要改进针对水环境问题的计算方案，这些方案针对具有并行处理能力的计算机进行优化，可以解决复杂流态和移动问题。床和边界。该研究项目的目标是提高计算方案的准确性和性能，以实现 3D 非静水流和移动床和边界沉积物输送的完全耦合模拟。该研究计划包括两个轴：增强时间积分方案的开发，以及专门为水平尺度通常大于垂直尺度的沿海和河流应用而设计的空间离散化方法。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的实现能力。在这些方案中，沉积物输送方程和流动方程将以完全耦合的形式求解，并且该模型将能够模拟复杂的流态，例如混合亚/超/跨临界流。 所提出的数值模型的一个重要特征是能够执行耦合 2D/3D 模拟，这将使其适用于并有效地解决涉及尖锐表面梯度、快速侵蚀/沉积和移动边界的各种工程问题。本研究提出的方法可应用于许多实际问题，包括快速冲刷问题，例如严重风暴潮或海啸引起的建筑物周围侵蚀、山洪引起的桥墩周围冲刷、尾矿坝溃决等其他应用包括预警系统以及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、数值建模者和决策者进行风险管理应用以及水利基础设施的设计和维护，以应对日益严重的极端降水、洪水和风暴潮，通常会导致快速侵蚀和沉积。