Variational assimilation of POD low-order dynamical systems

With this work, we propose improvements to the construction of low-order dynamical systems (LODS) for incompressible turbulent external flows. The model is constructed by means of a proper orthogonal decomposition (POD) basis extracted from experimental data. The POD modes are used to formulate an ordinary differential equation (ODE) system or a dynamical system which contains the main features of the flow. This is achieved by applying a Galerkin projection to the Navier–Stokes equations. Usually, the obtained LODS presents stability problems due to modes truncation and numerical uncertainties, specially when working on experimental data. We perform the model closure with a variational method, data assimilation, which refines the state variables within an iterative scheme. The technique allows as to correct the dynamic system coefficients and to identify and ameliorate the issued experimental data.

Keywords:

• Low-order dynamical systems
• Proper orthogonal decomposition
• Variational assimilation
• Dynamic system coefficients
• Incompressible cylinder flow
• PIV filtering

Notes

^†The linearization is equivalent to the Gâteaux derivative defined previously.