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

Authors:

Juan Du ^a,c, I.M. Navon ^b,？, Jiang Zhu ^a, Fangxin Fang  ^c, A.K. Alekseev ^d
a Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
^b Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA
^c Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College, Prince Consort Road, London SW7 2BP, UK
^d Moscow Institute of Physics and Technology, Moscow 141700, Russia 

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. 

Keywords：

Parabolized Navier–Stokes (PNS); Proper Orthogonal Decomposition (POD); Cost functional; Ad-hoc adaptive POD 4D VAR; Trust region POD 4D VAR

Citation:

J. Du et al. Reduced order modeling based on POD of a parabolized Navier–Stokes equations model II: Trust region POD 4D VAR data assimilation.Computers and Mathematics with Applications 65 (2013) 380–394 doi:10.1016/j.camwa.2012.06.001