A Computational Study of the Nudging Approach to Data Assimilation

数据同化助推方法的计算研究

• 批准号: 1818754
• 负责人: Michael Jolly
• 金额: $ 15万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818754&HistoricalAwards=false
• 关键词: Computational; Study; Nudging; Approach; Data

This work develops and tests new approaches to assimilating data into mathematical models to achieve more accurate prediction, for example in weather forecasts. The novelty is to consider data that is (a) concentrated in a small region (as over a metropolitan area), (b) moving (as from satellites, commercial airplanes, cars, even cell phones), and (c) from easily-measured quantities, such as atmospheric pressure. Numerical experiments will be supported by rigorous mathematical analysis.This work involves computational projects that tie together data assimilation, determining forms, and turbulence. The data assimilation is by nudging, an approach that has proven to be conducive to rigorous mathematical analysis but has undergone much less computational testing than have Kalman filters. Nudging is closely related to determining forms, ordinary differential equations in trajectory spaces that capture the global attractors of systems such as the Navier-Stokes equations of fluid flow. Such systems are expected to display turbulent behavior, which raises a particular set of computational issues addressed by this research.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.

这项工作开发并测试了将数据吸收到数学模型中的新方法，以实现更准确的预测，例如天气预报。 新颖之处在于考虑以下数据：（a）集中在一个小区域（如大都市区），（b）移动（如来自卫星、商用飞机、汽车，甚至手机），以及（c）来自容易测量的量，例如大气压力。数值实验将得到严格的数学分析的支持。这项工作涉及将数据同化、确定形式和湍流结合在一起的计算项目。数据同化是通过微移进行的，这种方法已被证明有利于严格的数学分析，但所经历的计算测试比卡尔曼滤波器要少得多。微移与确定形式、轨迹空间中的常微分方程密切相关，这些方程捕获系统的全局吸引子，例如流体流动的纳维-斯托克斯方程。此类系统预计会表现出湍流行为，从而引发本研究解决的一系列特定计算问题。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点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

On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces

• DOI: 10.3934/cpaa.2021169
• 发表时间: 2021-05
• 期刊: Communications on Pure & Applied Analysis
• 影响因子: 1
• 作者: M. Jolly;Anuj Kumar;V. Martinez

Continuous data assimilation for the 3D Ladyzhenskaya model: analysis and computations

3D Ladyzhenskaya 模型的连续数据同化：分析和计算

• DOI: 10.1016/j.nonrwa.2022.103659
• 发表时间: 2022
• 期刊: Nonlinear Analysis: Real World Applications
• 作者: Cao, Yu;Giorgini, Andrea;Jolly, Michael;Pakzad, Ali
• 通讯作者: Pakzad, Ali

Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations

二维磁流体动力学方程数据同化的数值效果研究

• DOI: 10.3934/jcd.2019006
• 发表时间: 2019
• 期刊: Journal of computational dynamics
• 影响因子: 1
• 作者: Hudson, Joshua;Jolly, Michael
• 通讯作者: Jolly, Michael

Tracer turbulence: the Batchelor--Howells--Townsend spectrum revisited

示踪湍流：重新审视巴彻勒-豪厄尔斯-汤森谱

• DOI: 10.1007/s00021-019-0478-6
• 发表时间: 2020
• 期刊: Journal of mathematical fluid mechanics
• 影响因子: 1.3
• 作者: Jolly, M. S.;Wirosoetisno, D.
• 通讯作者: Wirosoetisno, D.

Algebraic bounds on the Rayleigh–Bénard attractor

Rayleigh-Bénard 吸引子的代数界

• DOI: 10.1088/1361-6544/abb1c6
• 发表时间: 2021
• 期刊: Nonlinearity
• 影响因子: 1.7
• 作者: Cao, Yu;Jolly, Michael S;Titi, Edriss S;Whitehead, Jared P
• 通讯作者: Whitehead, Jared P