Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study
Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study
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DOI：
10.1007/s10915-018-0686-x
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发表时间：
2017-09
影响因子：
2.5
通讯作者：
A. Farhat;Hans Johnston;M. Jolly;E. Titi
中科院分区：
文献类型：
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作者：
A. Farhat;Hans Johnston;M. Jolly;E. Titi
我们介绍了一种连续（降尺度）的数据同化算法，用于仅使用涡度或局部环流测量的二维b<s:1>对流问题。在该算法中，在涡度方程中加入推入项对模型进行约束。数值结果表明，当仅同化空间粗粒涡度测量值时，该算法的近似解收敛于二维b<s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1> <s:1>)对流问题测量值对应的未知参考解（涡度和温度）。此外，这种收敛是使用比满足严格分析估计所需的分辨率更粗糙的数据来实现的。
We introduce a continuous (downscaling) data assimilation algorithm for the 2D Bénard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to constrain the model. Our numerical results indicate that the approximate solution of the algorithm is converging to the unknown reference solution (vorticity and temperature) corresponding to the measurements of the 2D Bénard convection problem when only spatial coarse-grain measurements of vorticity are assimilated. Moreover, this convergence is realized using data which is much more coarse than the resolution needed to satisfy rigorous analytical estimates.