LES-ROMs

In our group, we have been trying to bridge two research fields: reduced order modeling (ROM) and large eddy simulation (LES). We use explicit spatial filtering to construct ROM closure models of LES type. We develop structural, functional, data-driven, and hybrid ROM closure models. We also prove theorems about their stability and accuracy.

Data-Driven Variational Multiscale ROM

In this hybrid ROM framework, we use the classical Galerkin projection to model the evolution of the dominant modes and a data-driven approach to model the effect of the discarded modes (i.e., to solve the ROM closure problem). We leverage spatial filtering to find an explicit formula for the ROM closure term, and we utilize data and a least-squares problem to find the unknown parameters in the model form of the ROM closure model.