Geodesic
A component-based data assimilation strategy with applications to vascular flows
Duc-Quang Bui1 ; Pierre Mollo2 ; Fabio Nobile3 ; Tommaso Taddei4
1 Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539, USPN
2 Laboratoire de Mathématiques de Reims, CNRS UMR 9008, URCA
3 École Polytechnique Fédérale de Lausanne (EPFL), CSQI-MATH
4 IMB, UMR 5251, Univ. Bordeaux, 33400, Talence, France; INRIA, Inria Bordeaux Sud-Ouest, Team MEMPHIS, 33400, Talence, France
ESAIM. Proceedings, Tome 73 (2023), pp. 89-106.

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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.
DOI : 10.1051/proc/202373089

Duc-Quang Bui 1 ; Pierre Mollo 2 ; Fabio Nobile 3 ; Tommaso Taddei 4

1 Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539, USPN
2 Laboratoire de Mathématiques de Reims, CNRS UMR 9008, URCA
3 École Polytechnique Fédérale de Lausanne (EPFL), CSQI-MATH
4 IMB, UMR 5251, Univ. Bordeaux, 33400, Talence, France; INRIA, Inria Bordeaux Sud-Ouest, Team MEMPHIS, 33400, Talence, France 
@article{EP_2023_73_a5,
     author = {Duc-Quang Bui and Pierre Mollo and Fabio Nobile and Tommaso Taddei},
     title = {A component-based data assimilation strategy with applications to vascular flows},
     journal = {ESAIM. Proceedings},
     pages = {89--106},
     publisher = {mathdoc},
     volume = {73},
     year = {2023},
     doi = {10.1051/proc/202373089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202373089/}
}
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Duc-Quang Bui; Pierre Mollo; Fabio Nobile; Tommaso Taddei. A component-based data assimilation strategy with applications to vascular flows. ESAIM. Proceedings, Tome 73 (2023), pp. 89-106. doi : 10.1051/proc/202373089. http://geodesic.mathdoc.fr/articles/10.1051/proc/202373089/

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