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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 359606, 12 pages
http://dx.doi.org/10.1155/2014/359606
Research Article

Sensitivity Analysis of Unsteady Flow Fields and Impact of Measurement Strategy

1Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai 980-8577, Japan
2Institute of Fluid Science, Tohoku University, Sendai 980-8577, Japan

Received 5 March 2014; Revised 23 June 2014; Accepted 24 June 2014; Published 20 July 2014

Academic Editor: Bo Yu

Copyright © 2014 Takashi Misaka and Shigeru Obayashi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Difficulty of data assimilation arises from a large difference between the sizes of a state vector to be determined, that is, the number of spatiotemporal mesh points of a discretized numerical model and a measurement vector, that is, the amount of measurement data. Flow variables on a large number of mesh points are hardly defined by spatiotemporally limited measurements, which poses an underdetermined problem. In this study we conduct the sensitivity analysis of two- and three-dimensional vortical flow fields within a framework of data assimilation. The impact of measurement strategy, which is evaluated by the sensitivity of the 4D-Var cost function with respect to measurements, is investigated to effectively determine a flow field by limited measurements. The assimilation experiment shows that the error defined by the difference between the reference and assimilated flow fields is reduced by using the sensitivity information to locate the limited number of measurement points. To conduct data assimilation for a long time period, the 4D-Var data assimilation and the sensitivity analysis are repeated with a short assimilation window.