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We use approximate Bayesian computation (ABC) combined with an "improved"Markov chain Monte Carlo (IMCMC) method to estimate posterior distributions ofmodel parameters in subgrid-scale (SGS) closures for large eddy simulations(LES) of turbulent flows. The ABC-IMCMC approach avoids the need to directlycompute a likelihood function during the parameter estimation, enabling asubstantial speed-up and greater flexibility as compared to full Bayesianapproaches. The method also naturally provides uncertainties in parameterestimates, avoiding the artificial certainty implied by many optimizationmethods for determining model parameters. In this study, we outline details ofthe present ABC-IMCMC approach, including the use of an adaptive proposal and acalibration step to accelerate the parameter estimation process. We demonstratethe approach by estimating parameters in two nonlinear SGS closures usingreference data from direct numerical simulations of homogeneous isotropicturbulence. We show that the resulting parameter values give excellentagreement with reference probability density functions of the SGS stress andkinetic energy production rate in a priori tests, while also providing stablesolutions in forward LES (i.e., a posteriori tests) for homogeneous isotropicturbulence. The ABC-IMCMC method is thus shown to be an effective and efficientapproach for estimating unknown parameters, including their uncertainties, inSGS closure models for LES of turbulent flows.

Parameter Estimation for Subgrid-Scale Models Using Markov Chain Monte Carlo Approximate Bayesian Computation