Ninth Annual Graduate Student Miniconference in Computational Mathematics
Changhong Mou
Virginia Tech http://www.math.vt.edu/people.php?type=Graduates&pid=cmou 

Abstract 
Datadriven filtered reduced order modeling
We propose a datadriven filtered reduced order model (DDFROM) framework for the numerical simulation of fluid flows. The novel DDFROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the nonlinear PDE and construct a filtered ROM. This filtered ROM is low dimensional, but is not closed (because of the nonlinearity in the given PDE). (ii) In the second step, we use datadriven modeling to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved modes. To this end, we use a quadratic ansatz to model this interaction and close the filtered ROM. To find the new coefficients in the closed filtered ROM, we solve an optimization problem that minimizes the difference between the full order model data and our ansatz. We emphasize that the new DDFROM is built on general ideas of spatial filtering and optimization and is independent of (restrictive) phenomenological arguments, such as eddy viscosity. 