论文标题
使用局部可观察物的Navier-Stokes方程的数据同化
Data assimilation for the Navier-Stokes equations using local observables
论文作者
论文摘要
我们基于纯粹的局部观测值开发，分析和测试一个近似的全局数据同步/同步算法，该算法的局部观察结果是圆环上二维Navier-Stokes方程。我们证明，对于任何误差阈值，如果参考流是具有足够大的分析性半径分析性的，则可以在该阈值内恢复。包括数值计算以证明这种方法的有效性以及具有有关移动子域的数据的变体。特别是，我们以数值证明了从一小部分域收集的移动数据实现机器精度同步。
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.
