Predictive flow-field estimation

We are considering the problem of real-time prediction of 3D turbulent velocity fields based on a small number of scalar measurements. The method of proper orthogonal decomposition (POD) allows for the decomposition of an ensemble of velocity fields into a set of spatial basis functions and a set of temporal coefficients. The computation of the temporal coefficients is by no means a trivial matter, especially when one is faced with a large number of modes. In this paper we discuss the use of radial basis function (RBF) models to capture the discrete time evolution and nonlinear dynamics of the POD coefficients. Further, we propose the use of regularized regression techniques to generate models that provide mappings between the POD coefficients and scalar measurements. As a final step towards real-time prediction, the state–space RBF models and regression measurement models are combined using unscented Kalman filters to produce optimal solutions such that a balance between the state models and measurement models is achieved.The proposed methods are tested for two specific cases. The classical Lorenz model is chosen to demonstrate the use and effectiveness of RBF models as a potential candidate for state models. Flow around a wall-mounted cube in a channel at Re=20,000Re=20,000 is considered as the second case. The aim for the second case is to be able to accurately predict the POD coefficients outside the ensemble. It is shown that a large number of POD coefficients is required to approximate the velocity fields with sufficient accuracy. The RBF models are created based on only the temporal information available from the initial ensemble, and it is shown that the RBF model is able to correctly approximate the high-dimensional phase space. Combined with the unscented Kalman filter it is indeed possible to track the evolution of the POD coefficients for a long time. The robustness of the filter is demonstrated by considering the presence of noise in measurements and using measurement information at time steps greater than the evolution time step.