Orateur
Description
In this talk, I will survey reduced order model (ROM) closures and
stabilizations for under-resolved turbulent flows. Over the past
decade, several closure and stabilization strategies have been
developed to tackle the ROM inaccuracy in the convection-dominated,
under-resolved regime, i.e., when the number of degrees of freedom is
too small to capture the complex underlying dynamics. I will present
regularized ROMs, which are stabilizations that employ spatial
filtering to alleviate the spurious numerical oscillations generally
produced by standard ROMs in the convection-dominated, under-resolved
regime. I will also survey three classes of ROM closures, i.e.,
correction terms that increase the ROM accuracy: (i) functional
closures, which are based on physical insight; (ii) structural
closures, which are developed by using mathematical arguments; and
(iii) data-driven closures, which leverage available data. Throughout
my talk, I will highlight the impact made by data on classical
numerical methods over the past decade. I will also emphasize the role
played by physical constraints in data-driven modeling of ROM closures
and stabilizations.
