Efficient Numerical Simulations of Oceanic Flows with Application to Coastal Modeling

海洋流动的高效数值模拟及其在海岸建模中的应用

• 批准号: 1913073
• 负责人: Zhu Wang
• 金额: $ 16.79万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-15 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913073&HistoricalAwards=false
• 关键词: Efficient; Numerical; Simulations; Oceanic; Flows

Coastal ocean modeling has been developed for better serving climate impact assessments that are closely related to pressing society problems such as coastal flooding. To resolve multiple scales in ocean circulations and deal with complicated coastal topography, it is quite natural to use multi-resolution meshes in numerical simulations of oceanic flows. Typically, the grid sizes would vary from 100 km in major ocean basins to 1km in coastal regions. This, however, brings grand computational challenges: During explicit time integrations, the time step size would be restricted by the smallest grid size in the entire domain. Such a small time step size would make the numerical simulations unaffordable, especially for the purpose of climate modeling because long-term simulations are needed in such applications. To overcome this issue, this project puts forth new schemes that will be substantially more efficient compared to current algorithms used in ocean models while keeping their fidelity. This award will support one graduate student each year.We propose innovative, efficient numerical methods for simulating oceanic flows with application to coastal modeling. The new approaches comprise two major mathematical and computational developments: (i) conservative local time stepping, which allows the use of spatially-variable time step sizes in regions of different resolutions while keeping desired physical quantities conserved; and (ii) structure-preserving reduced order modeling, which significantly decreases the spatial dimension while maintaining the inherent Hamiltonian structure in the resultant low dimensional model. These approaches provide fast yet accurate and stable numerical solvers for simulating oceanic flow problems, which would enhance the simulation capability of current coastal ocean modeling and further increase computational efficiency required to solve pressing society problems such as coastal flooding. As a first step, we will study the shallow water equations on an unstructured, multi-resolution mesh. The effectiveness of the proposed methods will be demonstrated by verifying their stability and numerical accuracy. More complicated test cases and real-world applications will be further considered in this project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

沿海海洋模型的发展是为了更好地服务于与沿海洪水等紧迫社会问题密切相关的气候影响评估。为了解决海洋环流的多尺度问题和处理复杂的海岸地形，在海洋流动数值模拟中使用多分辨率网格是很自然的。通常，网格大小从主要海洋盆地的100公里到沿海地区的1公里不等。然而，这带来了巨大的计算挑战：在显式时间积分期间，时间步长将受到整个域中最小网格大小的限制。如此小的时间步长将使数值模拟难以承受，特别是对于气候模拟而言，因为在此类应用中需要长期模拟。为了克服这个问题，该项目提出了新的方案，与目前在海洋模型中使用的算法相比，这些方案将大大提高效率，同时保持其保真度。该奖项每年将资助一名研究生。我们提出了创新的、有效的数值方法来模拟海洋流动，并将其应用于海岸模拟。新方法包括两个主要的数学和计算发展：(i)保守的局部时间步进，它允许在不同分辨率的区域使用空间可变的时间步长，同时保持所需的物理量守恒；（ii）保留结构的降阶建模，在保持低维模型固有哈密顿结构的同时显著降低了空间维数。这些方法为模拟海洋流动问题提供了快速、准确和稳定的数值解，将增强当前沿海海洋建模的模拟能力，进一步提高解决沿海洪水等紧迫社会问题所需的计算效率。作为第一步，我们将在非结构化的多分辨率网格上研究浅水方程。本文将通过验证所提方法的稳定性和数值精度来证明其有效性。本项目将进一步考虑更复杂的测试用例和实际应用程序。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

POD-(H)DG Method for Incompressible Flow Simulations

• DOI: 10.1007/s10915-020-01328-4
• 发表时间: 2020-04
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: G. Fu;Zhu Wang

A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations

用于加速数值模拟的 FOM/ROM 混合方法

• DOI: 10.1007/s10915-021-01668-9
• 发表时间: 2021
• 期刊: Journal of Scientific Computing
• 影响因子: 2.5
• 作者: Feng, Lihong;Fu, Guosheng;Wang, Zhu
• 通讯作者: Wang, Zhu

A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems in unsteady convection-diffusion PDEs

• DOI: 10.1016/j.amc.2021.126750
• 发表时间: 2022-03
• 期刊: Appl. Math. Comput.
• 作者: Jun Liu;Zhu Wang

Numerical investigation of ensemble methods with block iterative solvers for evolution problems

• DOI: 10.3934/dcdsb.2020132
• 发表时间: 2020
• 期刊: Discrete & Continuous Dynamical Systems - B
• 作者: L. Ju;W. Leng;Zhu Wang;Shuai Yuan

High order explicit local time stepping methods for hyperbolic conservation laws

• DOI: 10.1090/mcom/3507
• 发表时间: 2019-05
• 期刊: Math. Comput.
• 作者: Thi-Thao-Phuong Hoang;L. Ju;W. Leng;Zhu Wang