Ninth Annual Graduate Student Miniconference in Computational Mathematics
Muhammad Mohebujjaman
Virginia Tech https://www.math.vt.edu/people/jaman/ 

Abstract 
Physicallyconstrained datadriven reduced order modeling of fluid flows
In this talk, we present two approaches for enforcing better conservation properties for reduced order models (ROMs) of fluid flows. In the first approach, to construct the centering trajectory, we use the Stokes extension instead of the standard snapshot average. We show that the Stokes extension yields significantly more accurate results. In the second approach, we enforce physical constraints in the datadriven modeling of the ROM closure term. The constrained datadriven ROM is significantly more accurate than its unconstrained counterpart. 