Reduced order modeling based on POD of a parabolized Navier-Stokes equations model II: Trust region POD 4D VAR data assimilation

Authors:
Juan Du;I. M. Navon;Jiang Zhu;Fangxin Fang;A. K. Alekseev
Affiliations:
Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China and Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College, Pri ...;Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA;Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College, Prince Consort Road, London SW7 2BP, UK;Moscow Institute of Physics and Technology, Moscow 141700, Russia
Venue:
Computers & Mathematics with Applications
Year:
2013

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Abstract

A reduced order model based on Proper Orthogonal Decomposition (POD) 4D VAR (Four-dimensional Variational) data assimilation for the parabolized Navier-Stokes (PNS) equations is derived. Various approaches of POD implementation of the reduced order inverse problem are studied and compared including an ad-hoc POD adaptivity along with a trust region POD adaptivity. The numerical results obtained show that the trust region POD 4D VAR provides the best results amongst all the POD adaptive methods tested in all error metrics for the reduced order inverse problem of the PNS equations.