A Bayesian fusion model for space-time reconstruction of finely resolved velocities in turbulent flows from low resolution measurements. (9th October 2015) - Van Nguyen, Linh; Laval, Jean-Philippe; Chainais, Pierre
Abstract: The study of turbulent flows calls for measurements with high resolution in both space and time. We propose a new approach to reconstruct high-temporal–high-spatial resolution velocity fields by combining two sources of information that are well resolved either in space or in time, the low-temporal–high-spatial (LTHS) and the high-temporal–low-spatial (HTLS) resolution measurements. In the framework of co-conception between sensing and data post-processing, this work extensively investigates a Bayesian reconstruction approach using a simulated database. A Bayesian fusion model is developed to solve the inverse problem of data reconstruction. The model uses a maximum a posteriori estimate, which yields the most probable field knowing the measurements. The direct numerical simulation (DNS) of a wall-bounded turbulent flow at moderate Reynolds number is used to validate and assess the performances of the present approach. Low-resolution measurements are subsampled in time and space from the fully resolved data. Reconstructed velocities are compared to the reference DNS to estimate the reconstruction errors. The model is compared to other conventional methods such as linear stochastic estimation and cubic spline interpolation. Results show the superior accuracy of the proposed method in all configurations. Further investigations of model performances on various scales demonstrate its robustness. Numerical experiments also permit one to estimate the expected maximum information level corresponding to limitations of experimental instruments.