Augmented Prediction of Turbulent Flows via Sequential Estimators

A sensitivity analysis of new methodological approaches for state estimation (Meldi and Poux J. Comput. Phys. 347, 207–234, 2017) is proposed in this manuscript. The performance of the estimator is tested via the analysis of a number of aspects that play a major role in the augmented prediction process, such as the density in time sampling of available observation, the placement of sensors and the interaction with boundary conditions. The work is developed for the turbulent spatially evolving mixing layer test case, using high precision DNS samples as observation and Smagorinsky LES as underlying model. A number of estimators combining LES with DNS data integrated via sensors are performed, varying the frequency of time sampling of observation f_T = 1/Δ_T, where Δ_T is the period between successive assimilation phases. It is concluded that if Δ_T ≤≈ 0.5t_A, where t_A is the characteristic average advection time, the prediction via estimator shows minimal differences i.e. the process of state estimation has reached convergence. This relation can be interpreted as a threshold for converged state estimation. However, the results show as well that a linear converge towards pure model performance is not obtained for every physical quantity with progressive decrease of f_T, while eventually pure model results are obtained for f_T → 0. In addition, the effect of upstream boundary conditions over the state estimation are investigated and strategies for optimized positions of sensors are derived.