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Linear and Nonlinear Data Assimilation in Turbulent Systems

湍流系统中的线性和非线性数据同化

基本信息

批准号：
1716801
负责人：
Adam Larios
金额：
$ 14.01万
依托单位：
University of Nebraska-Lincoln
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-15 至 2020-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1716801&HistoricalAwards=false
关键词：
Linear Nonlinear Data Assimilation Turbulent

项目摘要

Turbulent flows play a fundamental role in weather and climate dynamics, which are major factors impacting environmental stability, agricultural production, civil infrastructure, and other important areas. Turbulence is highly chaotic, and therefore modern approaches to predicting its behavior are based on simulations. A major difficulty in accurately simulating turbulent flows is the problem of determining the initial state of the flow. For example, weather prediction models typically require the present state of the weather as input. However, the state of the weather is only measured at certain points, such as at the locations of weather stations or weather satellites. Data assimilation makes up for the lack of complete knowledge of the initial state. It incorporates incoming data into the equations, driving the simulation to the correct solution. The objective of this project is to develop innovative computational and mathematical methods to test, improve, and extend a promising new class of algorithms for data assimilation in turbulent flows. Results of this work increase predictive capabilities of scientists, produce new mathematical and computational tools, and help educate students in challenging new areas with real-world impacts. A student participates in the work of the project.The project focuses on major areas of research aimed at making a new data assimilation tool as useful as possible to researchers in fluid dynamics and geophysics. Firstly, an in-depth analytical and computational study of new nonlinear versions of the data assimilation algorithm is carried out, and its convergence rates are carefully estimated. Secondly, the investigator carries out the first 3D simulations using the new algorithm in the context of the incompressible Navier-Stokes equations of fluids, and makes a detailed comparison of the method with cutting-edge data assimilation methods. Finally, the method is extended to multi-physics settings to include fluids driven by heat convection and fluids with magnetic properties. A student participates in the work of the project.

湍流在天气和气候动力学中发挥着重要作用，是影响环境稳定、农业生产、民用基础设施和其他重要领域的主要因素。湍流是高度混乱的，因此预测其行为的现代方法是基于模拟的。精确模拟湍流的一个主要困难是确定流动的初始状态问题。例如，天气预报模型通常需要当前的天气状态作为输入。然而，天气状况只能在某些点测量，例如气象站或气象卫星的位置。数据同化弥补了对初始状态缺乏完整知识的不足。它将输入的数据整合到方程中，推动模拟得到正确的解决方案。该项目的目标是开发创新的计算和数学方法来测试、改进和扩展一类有前途的新算法，用于湍流中的数据同化。这项工作的结果提高了科学家的预测能力，产生了新的数学和计算工具，并帮助教育学生挑战具有现实世界影响的新领域。一名学生参与该项目的工作。该项目侧重于主要研究领域，目的是使一种新的数据同化工具尽可能对流体动力学和地球物理学的研究人员有用。首先，对新的非线性数据同化算法进行了深入的分析和计算研究，并对其收敛速度进行了仔细的估计。其次，在不可压缩流体Navier-Stokes方程的背景下，利用新算法进行了首次三维仿真，并与前沿数据同化方法进行了详细比较。最后，将该方法扩展到多物理场环境，包括热对流驱动流体和具有磁性的流体。一名学生参与该项目的工作。