Streamline derivative projection-based POD-ROM for convection-dominated flows. Part I : Numerical Analysis
This work offers a theoretically grounded ROM for convection-dominated flows, which is important for computational fluid dynamics practitioners seeking accurate and efficient simulations.
The paper introduces improved Reduced Order Models (ROM) for convection-dominated flows by incorporating stabilization techniques from Large Eddy Simulations (LES) into Proper Orthogonal Decomposition (POD) with Galerkin projection. It provides numerical analysis with error estimates and an efficient implementation using DEIM.
We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection Stabilization (LPS), applied to standard models created by Proper Orthogonal Decomposition (POD) of flows with Galerkin projection. The numerical analysis of the fully Navier-Stokes discretization for the proposed new POD-ROM is presented, by mainly deriving the corresponding error estimates. Also, we suggest an efficient practical implementation of the stabilization term, where the stabilization parameter is approximated by the Discrete Empirical Interpolation Method (DEIM).