A Component-Based Data Assimilation Strategy with Applications to Vascular Flows

Duc-Quang Bui (1) , Pierre Mollo (2) , Fabio Nobile (3) , Tommaso Taddei (4)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LMR - Laboratoire de Mathématiques de Reims
3 EPFL - Ecole Polytechnique Fédérale de Lausanne
4 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS

We present a parameterized-background data-weak (PBDW) approach [Y Maday, AT Patera, JD Penn, M Yano, Int J Numer Meth Eng, 102(5), 933-965] to the steady-state variational data assimilation (DA) problem for systems modeled by partial differential equations (PDEs) and characterized by multiple interconnected components, with emphasis on vascular flows. We focus on the problem of reconstructing the state of the system in one specific component, based on local measurements. The PBDW approach does not require the solution of any PDE model at prediction stage (projection-by-data) and, as such, enables local state estimates on single components, as long as good background and update spaces for the estimation can be constructed. We discuss the application of PBDW to a two-dimensional steady Navier-Stokes problem for a family of parameterized geometries, and investigate instead the effects of enforcing no-slip boundary conditions and incompressibility constraints on the background and update spaces to enhance the state estimation. Furthermore, we show an actionable strategy to train local reduced-order bases (ROBs) for the background space that can later be used for DA tasks.

Domaines: Analyse numérique [math.NA]

Duc-Quang Bui, Pierre Mollo, Fabio Nobile, Tommaso Taddei. A Component-Based Data Assimilation Strategy with Applications to Vascular Flows. ESAIM: Proceedings and Surveys, inPress, 73, pp.89-106. ⟨10.1051/proc/202373089⟩. ⟨hal-03884154v1⟩