二维磁流体动力学方程数据同化的数值有效性研究

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2019-08-01 DOI:10.3934/JCD.2019006

Joshua Hudson, M. Jolly

{"title":"二维磁流体动力学方程数据同化的数值有效性研究","authors":"Joshua Hudson, M. Jolly","doi":"10.3934/JCD.2019006","DOIUrl":null,"url":null,"abstract":"We study the computational efficiency of several nudging data assimilation algorithms for the 2D magnetohydrodynamic equations, using varying amounts and types of data. We find that the algorithms work with much less resolution in the data than required by the rigorous estimates in [ 7 ]. We also test other abridged nudging algorithms to which the analytic techniques in [ 7 ] do not seem to apply. These latter tests indicate, in particular, that velocity data alone is sufficient for synchronization with a chaotic reference solution, while magnetic data alone is not. We demonstrate that a new nonlinear nudging algorithm, which is adaptive in both time and space, synchronizes at a super exponential rate.","PeriodicalId":37526,"journal":{"name":"Journal of Computational Dynamics","volume":"34 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2019-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations\",\"authors\":\"Joshua Hudson, M. Jolly\",\"doi\":\"10.3934/JCD.2019006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the computational efficiency of several nudging data assimilation algorithms for the 2D magnetohydrodynamic equations, using varying amounts and types of data. We find that the algorithms work with much less resolution in the data than required by the rigorous estimates in [ 7 ]. We also test other abridged nudging algorithms to which the analytic techniques in [ 7 ] do not seem to apply. These latter tests indicate, in particular, that velocity data alone is sufficient for synchronization with a chaotic reference solution, while magnetic data alone is not. We demonstrate that a new nonlinear nudging algorithm, which is adaptive in both time and space, synchronizes at a super exponential rate.\",\"PeriodicalId\":37526,\"journal\":{\"name\":\"Journal of Computational Dynamics\",\"volume\":\"34 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2019-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/JCD.2019006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/JCD.2019006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}

引用次数: 14

摘要

利用不同数量和类型的数据，研究了几种推动数据同化算法对二维磁流体动力学方程的计算效率。我们发现，这些算法在数据中的分辨率远低于[7]中严格估计所需的分辨率。我们还测试了[7]中的分析技术似乎不适用的其他简化的助推算法。这些后一种测试特别表明，速度数据本身足以与混沌参考解同步，而磁数据本身则不够。本文提出了一种具有时间和空间自适应的非线性微推算法，该算法能以超指数速率同步。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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

We study the computational efficiency of several nudging data assimilation algorithms for the 2D magnetohydrodynamic equations, using varying amounts and types of data. We find that the algorithms work with much less resolution in the data than required by the rigorous estimates in [ 7 ]. We also test other abridged nudging algorithms to which the analytic techniques in [ 7 ] do not seem to apply. These latter tests indicate, in particular, that velocity data alone is sufficient for synchronization with a chaotic reference solution, while magnetic data alone is not. We demonstrate that a new nonlinear nudging algorithm, which is adaptive in both time and space, synchronizes at a super exponential rate.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.