Reducing sensors for transient heat transfer problems by means of variational data assimilation

Amina Benaceur (1, 2, 3, 4)

1 EDF - EDF
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
4 MIT - Department of Applied Mathematics

We propose a contribution that combines model reduction with data assimilation. A dedicated Parametrized Background Data-Weak (PBDW) [1] 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.

Domaines: Analyse numérique [math.NA]

Amina Benaceur. Reducing sensors for transient heat transfer problems by means of variational data assimilation. SMAI Journal of Computational Mathematics, 2021, 7, pp.1-25. ⟨10.5802/smai-jcm.68⟩. ⟨hal-02265533v2⟩