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Journal of Scientific Computing

, Volume 77, Issue 3, pp 1519–1533 | Cite as

Assimilation of Nearly Turbulent Rayleigh–Bénard Flow Through Vorticity or Local Circulation Measurements: A Computational Study

  • Aseel Farhat
  • Hans Johnston
  • Michael Jolly
  • Edriss S. Titi
Article

Abstract

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.

Keywords

Bénard convection Data assimilation Synchronization Turbulence 

Mathematics Subject Classification

34D06 76E06 76F35 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  3. 3.Department of MathematicsIndiana UniversityBloomingtonUSA
  4. 4.Department of MathematicsTexas A&M UniversityCollege StationUSA
  5. 5.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

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