Data assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements

In this paper we propose a continuous data assimilation (downscaling) algorithm for the Bénard convection in porous media using only discrete spatial-mesh measurements of the temperature. In this algorithm, we incorporate the observables as a feedback (nudging) term in the evolution equation of the...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 438; no. 1; pp. 492 - 506
Main Authors Farhat, Aseel, Lunasin, Evelyn, Titi, Edriss S.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2016
Subjects
Bénard convection
Continuous data assimilation
Downscaling
Nudging
Porous media
Signal synchronization
Porous media
Signal synchronization
Bénard convection
Continuous data assimilation
Downscaling
Nudging
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Summary:In this paper we propose a continuous data assimilation (downscaling) algorithm for the Bénard convection in porous media using only discrete spatial-mesh measurements of the temperature. In this algorithm, we incorporate the observables as a feedback (nudging) term in the evolution equation of the temperature. We show that under an appropriate choice of the nudging parameter and the size of the mesh, and under the assumption that the observed data is error free, the solution of the proposed algorithm converges at an exponential rate, asymptotically in time, to the unique exact unknown reference solution of the original system, associated with the observed (finite dimensional projection of) temperature data. Moreover, we note that in the case where the observational measurements are not error free, one can estimate the error between the solution of the algorithm and the exact reference solution of the system in terms of the error in the measurements.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.01.072