Probabilistic data-driven turbulence closure modeling by assimilating statistics

Journal article, 2025

A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model [8] and data assimilation methods. The method requires a posteriori measured data to define a stochastic large-eddy simulation model, which is combined with a Bayesian statistical correction enforcing user-specified statistics extracted from high-fidelity flow snapshots. Thus, it enables computationally cheap ensemble simulations by combining knowledge of the local integration error and knowledge of desired flow statistics. An example implementation of the modeling framework is given for two-dimensional Rayleigh-B & eacute;nard convection at Rayleigh number Ra = 1010, incorporating stochastic perturbations and an ensemble Kalman filtering step in a non-intrusive way. Physical flow dynamics are obtained, whilst kinetic energy spectra and heat flux are accurately reproduced in long-time ensemble forecasts on coarse grids for two discretizations. The model is shown to produce accurate results with as few as 20 high-fidelity flow snapshots as input data.