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以实现更准确预测的新方法，例如在天气预报中。 新颖性是要考虑（a）集中在一个小区域（如大都市区域），（b）移动（从卫星，商业飞机，汽车，甚至手机）和（c）从易于估量的数量（例如大气压力）移动的数据。数值实验将由严格的数学分析支持。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。数据同化是通过推动来的，这种方法已被证明有利于严格的数学分析，但经历了比Kalman过滤器要少得多的计算测试。 nuding与确定形式，轨迹空间中的普通微分方程密切相关，这些方程捕获了系统的全局吸引子，例如流体流的Navier-Stokes方程。预计此类系统将展示动荡的行为，该行为提出了本研究解决的一组特定的计算问题。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响来通过评估来支持的。

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

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.

A Determining Form for the 2D Rayleigh-Bénard Problem

• 发表时间: 2019-06
• 期刊: arXiv: Analysis of PDEs
• 作者: Yu Cao;M. Jolly;E. Titi

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