Strong and weak constraint variational assimilations for reduced order fluid flow modeling

Abstract

In this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows. Both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a Galerkin projection of the Navier Stokes equation. The techniques proposed differ in the control variables they involve. The first one introduces a weak dynamical model defined only up to an additional uncertainty time-dependent function whereas the second one, handles a strong dynamical constraint in which the dynamical system's coefficients constitute the control variables. Both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction. The techniques have been assessed on numerical data and for real experimental conditions with noisy Image Velocimetry data.

Optical Flow

“…See [141] for a corresponding approach to data assimilation [142]. A nice feature of this method is the ability to estimate initial conditions that are generally unknown, too.…”

Optical Flow

“…Such extensions appear more natural in connection with dynamic physical models constraining optical flow estimation, as opposed to stationary formulations like (88). See [141] for a corresponding approach to data assimilation [142]. A nice feature of this method is the ability to estimate initial conditions that are generally unknown, too.…”

POD-spectral decomposition for fluid flow analysis and model reduction

“…Thus the dynamics of chronos can be described as a summation along the different frequencies arising from the CK decomposition. Note that this gives an equivalent representation as the one would expect integrating equation (9). However it is important to outline that neither the precise form of the POD-Galerkin system, nor any specific assumption on boundary conditions on pressure has to be settled with this approach.…”

“…The wake behind a circular cylinder has been generated in the IRSTEA(Cemagref) wind tunnel. Experimental conditions are coincident with the same as those described in [9].…”

“…Some of them include additional dissipative models [12] or rely on nonlinear Galerkin projection techniques [1,4,13]. Robust techniques based on optimal control strategies have been also proposed for building reduced dynamical models from noisy data [9,15] and incomplete knowledge of the actual flow dynamics (i.e. unknown initial condition, unknown or partially known forcing terms,...).…”