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Journal of Computational Mathematics

Reducing sensors for transient heat transfer problems by means of variational data assimilation
Amina Benaceur1
1 Massachusetts Institute of Technology, Cambridge, USA. University Paris-Est, CERMICS (ENPC), 77455 Marne la Vallée Cedex 2 and INRIA Paris, 75589 Paris, France. EDF Lab Les Renardières, 77250 Ecuelles Cedex, France.
The SMAI Journal of computational mathematics, Volume 7 (2021), pp. 1-25.

We propose a contribution that combines model reduction with data assimilation. A dedicated Parametrized Background Data-Weak (PBDW) approach has been introduced in the literature so as to combine numerical models with experimental measurements. We extend the approach to a time-dependent framework by means of a POD-greedy reduced basis construction. Since the construction of the basis is performed offline, the algorithm addresses the time dependence of the problem while the time stepping scheme remains unchanged. Moreover, we devise a new algorithm that exploits offline state estimates in order to diminish both the dimension of the online PBDW statement and the number of required sensors collecting data. The idea is to exploit in situ observations in order to update the best-knowledge model, thereby improving the approximation capacity of the background space.

Published online:
DOI: 10.5802/smai-jcm.68
Classification: 65K10
Keywords: PBDW, model reduction, data assimilation, sensor reduction, heat transfer
Amina Benaceur 1

1 Massachusetts Institute of Technology, Cambridge, USA. University Paris-Est, CERMICS (ENPC), 77455 Marne la Vallée Cedex 2 and INRIA Paris, 75589 Paris, France. EDF Lab Les Renardières, 77250 Ecuelles Cedex, France.
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Reducing sensors for transient heat transfer problems by means of variational data assimilation},
     journal = {The SMAI Journal of computational mathematics},
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     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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Amina Benaceur. Reducing sensors for transient heat transfer problems by means of variational data assimilation. The SMAI Journal of computational mathematics, Volume 7 (2021), pp. 1-25. doi : 10.5802/smai-jcm.68. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.68/

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