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, Majid
• 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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=717822
• 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，例如液压结构周围的侵蚀，涉及尖锐的梯度，自由表面流动，移动边界，非静态压力，快速侵蚀/沉淀，在某些情况下是超临界流。对此类问题的有效和准确的模拟可以极大地改善液压基础设施的设计，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度的增加，非常需要改进针对水力环境问题特定的计算方案，这些问题针对具有并行处理能力的计算机进行了优化，并且可以解决复杂的流程和移动问题的问题床和边界。 该研究计划的目的是提高计算方案的准确性和性能，以完全耦合3D非静态流和沉积物传输以及移动的床和边界的沉积物传输。该研究计划包括两个轴：增强的时间整合方案的开发，以及专门为沿海和河流应用设计的空间离散方法的开发，在沿海和河流应用中，水平尺度通常大于垂直尺度。为此，将开发具有较高准确性和效率的新型优化数值方案，并特别强调大型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施的能力。在这些方案中，将以完全耦合的形式求解沉积物传输方程和流动方程，并且该模型将能够模拟复杂的流程度，例如混合的子/超级/超级/反临界流。 所提出的数值模型的一个重要特征是能够执行耦合的2D/3D模拟，这将使其适用且有效，适用于涉及尖锐表面梯度，快速侵蚀/沉积和移动边界的广泛工程问题。这项研究中提出的方法可以应用于许多实际问题，包括快速跑步问题，例如严重的暴风雨潮或海啸引起的结构周围侵蚀的问题，围绕着山洪造成的桥梁搜索，尾巴爆发，违反了山洪爆发。等等。其他应用程序包括预警系统以及对现场和实验室案例的实时模拟，其中该模型的速度和效率起着至关重要的作用。此外，这些高级建模工具可以帮助众多用户，包括设计师，数字建模者和风险管理应用程序的决策者，以及液压基础设施的设计和维护，以应对极端降水的强度，洪水泛滥的强度和暴风雨的潮流，这通常会导致快速侵蚀和沉积。