Data Assimilation for the Navier-Stokes Equations Using Local Observables
Data Assimilation for the Navier-Stokes Equations Using Local Observables
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DOI：
10.1137/20m136058x
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发表时间：
2020-08
期刊：
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通讯作者：
A. Biswas;Zachary Bradshaw;M. Jolly
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文献类型：
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作者：
A. Biswas;Zachary Bradshaw;M. Jolly
我们开发、分析和测试了一种近似的全局数据同化/同步算法，该算法基于环面上二维Navier-Stokes方程的纯局部观测。证明了对于任意误差阈值，如果参考流是解析的，且解析半径足够大，则在该阈值内可以恢复。数值计算证明了该方法的有效性，以及在移动子域上的数据变体。特别是，我们在数值上证明了从一小部分域收集的移动数据可以实现机器精度同步。
We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations on the torus. We prove that, for any error threshold, if the reference flow is analytic with sufficiently large analyticity radius, then it can be recovered within that threshold. Numerical computations are included to demonstrate the effectiveness of this approach, as well as variants with data on moving subdomains. In particular, we demonstrate numerically that machine precision synchronization is achieved for mobile data collected from a small fraction of the domain.