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

Abstract

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.

A component-based data assimilation strategy with applications to vascular flows

“…Our point of departure is the parameterized-background data-weak (PBDW) approach to state estimation. PBDW was first introduced in [17] and further extended and analyzed in several subsequent works [2,4,8,11,18,26]. The key idea of PBDW is to seek an approximation u = z + η of the state in the region of interest Ω, employing projection-by-data.…”