Physically-Constrained Data-Driven Correction for Reduced Order Modeling of Fluid Flows

Tuesday, June 19, 2018
Ora Inizio: 
Ora Fine: 
Traian Iliescu
Virginia Tech


We propose a data-driven correction reduced order model
(DDC-ROM) framework for the numerical simulation of fluid flows, which
can be formally written as DDC-ROM = Galerkin-ROM + Correction.  The new
DDC-ROM is constructed by using ROM spatial filtering and data-driven
ROM closure modeling (for the Correction term).  Furthermore, we propose
a physically-constrained DDC-ROM (CDDC-ROM), which aims at improving the
physical accuracy of the DDC-ROM.  The new physical constraints require
that the CDDC-ROM operators satisfy the same type of physical laws
(i.e., the Correction term's linear component should be dissipative and
the Correction term's nonlinear component should conserve energy) as
those satisfied by the fluid flow equations. To implement these physical
constraints, in the data-driven modeling step, we replace the
unconstrained least squares problem with a constrained least squares
problem.  We perform a numerical investigation of the new CDDC-ROM and
standard DDC-ROM for a 2D channel flow past a circular cylinder at
Reynolds numbers $Re=100, Re=500$, and $Re=1000$.  To this end, we
consider a reproductive regime as well as a predictive (i.e.,
cross-validation) regime in which we use as little as $50\%$ of the
original training data.  The numerical investigation clearly shows that
the new CDDC-ROM is significantly more accurate than the DDC-ROM in both