Applied math. talk: Large Eddy Simulation Reduced Order Models by Traian Iliescu, Virginia Tech

In this talk, we present reduced order models (ROMs) for turbulent flows,
which are constructed by using ideas from large eddy simulation (LES) and
variational multiscale (VMS) methods.  First, we give a
general introduction to reduced order modeling and emphasize the
connection to classical Galerkin methods (e.g., the finite element method)
and the central role played by data.  Then, we describe the closure
problem, which represents one of the main obstacles in the development of
ROMs for realistic, turbulent flows.  To tackle the ROM closure problem,
we use ROM spatial filters (e.g., the ROM projection and the ROM
differential filter) and build new LES-ROMs that capture the large scale
ROM features and model the interaction between these large scales and the
small scale ROM features. Finally, we present results for these LES-ROMs
in the numerical simulation of
under-resolved engineering flows (e.g., flow past a cylinder and
turbulent channel flow) and the quasi-geostrophic equations (which model
the large scale ocean circulation).