Model reduction by proper orthogonal decomposition for lambda-omega systems

Abstract

Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work POD is used to derive low-order models for a so-called lambda-omega system that is a universal model to investigate two-species reaction-diffusion problems. In the case of fast reaction kinetics and small diffusion, these systems evolve to turbulent behavior. The performance of the POD model reduction is studied in dependence on the parameters of the lambda-omega system. With increasing turbulence more POD modes are needed to capture the dynamics of the full system in a satisfactory way.