Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study
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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.
KeywordsBénard convection Data assimilation Synchronization Turbulence
Mathematics Subject Classification34D06 76E06 76F35
This work was initiated while the authors were visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the National Science Foundation (NSF). The work of A.F. is supported in part by NSF Grant DMS-1418911. The work of M.S.J. is supported in part by NSF Grant DMS-1418911 and Leverhulme Trust Grant VP1-2015-036. The work of E.S.T. is supported in part by the ONR Grant N00014-15-1-2333.
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