论文标题
2D Navier-Stokes方程的移动数据同化方案的收敛
Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations
论文作者
论文摘要
我们为周期性的2D Navier-Stokes方程引入了纽约数据同化算法的局部版本，其中将观测值（即本地化）限制在一个窗口中，该窗口以给定速度以预定的路径沿整个域移动。我们证明，如果运动足够快，则该算法与参考解决方案完美同步。分析表明，根据误差为主导的区域，亚域移动的知情方案是最佳的。介绍了数值模拟，以比较遵循常规模式的运动功效，以主导误差为指导，而一个是随机的。
We introduce a localized version of the nudging data assimilation algorithm for the periodic 2D Navier-Stokes equations in which observations are confined (i.e., localized) to a window that moves across the entire domain along a predetermined path at a given speed. We prove that, if the movement is fast enough, then the algorithm perfectly synchronizes with a reference solution. The analysis suggests an informed scheme in which the subdomain moves according to a region where the error is dominant is optimal. Numerical simulations are presented that compare the efficacy of movement that follows a regular pattern, one guided by the dominant error, and one that is random.
