Collaborative Research: Structure Preserving Numerical Methods for Hyperbolic Balance Laws with Applications to Shallow Water and Atmospheric Models

合作研究：双曲平衡定律的结构保持数值方法及其在浅水和大气模型中的应用

• 批准号: 1818666
• 负责人: Alexander Kurganov
• 金额: $ 5万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818666&HistoricalAwards=false
• 关键词: Collaborative; Research; Structure; Preserving; Numerical

This project will significantly contribute toward development of computational methods for shallow water and related models and will provide considerably more powerful tools for studying a variety of water waves and atmospheric phenomena. Special attention will be paid to applications arising in oceanography, atmospheric sciences, hydraulic, coastal, civil engineering, in which rapid changes in the bottom topography, Coriolis forces, friction, multiscale regimes, and uncertain phenomena factor heavily. The studied problems will include shallow water flows in multi-connected river channel systems, tsunami wave propagation and low Froude regime shallow water models, dynamics models of tropical cyclones and clouds with uncertain data.The newly developed tools may have a great potential in designing coastal protection systems and investigating the effects of sediment transport on shelf drilling platforms as well as contributing to a better prediction of tropical cyclones trajectories and tsunami wave propagation and on-shore arrival.The project focuses on development of new structure preserving numerical methods for hyperbolic balance laws with applications to shallow water equations and related models. Shallow water models are systems of time-dependent partial differential equations (PDEs) that are derived using physical properties such as conservation of mass and momentum, and hydrostatic or barotropic approximations. Naturally, these applications, especially in cases of high space dimensions, require development and implementation of special numerical methods that are not only consistent with the governing system of PDEs, but also preserve certain structural and asymptotic properties of the underlying problem at the discrete level. The development of new numerical techniques will be based on high-order shock-capturing finite-volume schemes, asymptotic preserving, adaptive moving mesh and stochastic Galerkin methods utilizing major advantages of each one of these methods in the context of studied problems. Besides providing examples that corroborate the numerical approach, the foregoing applications are of a substantial independent value for a broad class of problems arising in today's science.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.

该项目将有助于开发浅水和相关模型的计算方法，并为研究各种水波和大气现象提供更大的工具。将特别关注海洋学，大气科学，液压，沿海，土木工程的应用，其中底部地形，科里奥利部队，摩擦，多尺度制度以及不确定现象因素的快速变化在很大程度上变化。研究的问题将包括多连接的河道系统中的浅水流，海啸传播和低弗洛德政权浅水模型，具有不确定数据的热带气旋的动态模型和云的动态模型。新开发的工具可能具有巨大的潜力。保护系统并调查沉积物传输对货架钻孔平台的影响，并为更好地预测热带气旋轨迹和海啸波传播和近岸到达。应用于浅水方程和相关模型。浅水模型是使用物理特性（例如质量和动量保存）以及静水或压缩近似值等物理特性得出的时间依赖性部分微分方程（PDE）的系统。自然，这些应用程序，尤其是在高空间维度的情况下，需要开发和实施特殊的数值方法，这些方法不仅与PDE的管理系统一致，而且还需要在离散级别保留基本问题的某些结构和渐近性。新数值技术的开发将基于高阶冲击捕获有限量 - 体积方案，渐近保存，适应性移动网格和随机的盖金方法，利用了研究问题的上下文中每种方法的主要优势。除了提供证实数字方法的示例外，上述应用程序对于当今科学中引起的广泛问题具有实质性的独立价值。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和知识分子的优点和评估值得的支持。更广泛的影响审查标准。