Streamline derivative projection-based POD-ROM for convection-dominated flows. Part I : Numerical Analysis

TL;DR

This paper develops improved nonlinear reduced order models for convection-dominated flows using stabilization techniques inspired by LES, providing numerical analysis and efficient implementation strategies.

Contribution

It introduces a novel POD-ROM with stabilization inspired by LES, including error analysis and a practical DEIM-based stabilization parameter approximation.

Findings

Derived error estimates for the stabilized POD-ROM.

Proposed an efficient implementation of the stabilization term.

Validated the improved accuracy for convection-dominated flows.

Abstract

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).