Du, Juan; Navon, I. M.; Zhu, Jiang; Fang, Fangxin; Alekseev, A. K. Reduced order modeling based on POD of a parabolized Navier-Stokes equations model II: trust region POD 4D VAR data assimilation. (English) Zbl 1319.76030 Comput. Math. Appl. 65, No. 3, 380-394 (2013). Summary: 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. Cited in 24 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:parabolized Navier-Stokes (PNS); proper orthogonal decomposition (POD); cost functional; ad-hoc adaptive POD 4D VAR; trust region POD 4D VAR PDFBibTeX XMLCite \textit{J. Du} et al., Comput. Math. Appl. 65, No. 3, 380--394 (2013; Zbl 1319.76030) Full Text: DOI