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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

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.

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
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