Parameter Estimation for RANS Models Using Approximate Bayesian Computation

TL;DR

This paper introduces an efficient approximate Bayesian computation (ABC) method, ABC-IMCMC, for estimating and calibrating parameters in RANS turbulence models using diverse reference data, improving model accuracy.

Contribution

The paper develops and demonstrates ABC-IMCMC, an advanced ABC approach with calibration and MCMC, for faster, flexible RANS model parameter estimation without explicit likelihood calculations.

Findings

ABC-IMCMC improves RANS model calibration accuracy.

The method accelerates parameter estimation in complex turbulence models.

Demonstrated effectiveness on both simulation and experimental data.

Abstract

We use approximate Bayesian computation (ABC) to estimate unknown parameter values, as well as their uncertainties, in Reynolds-averaged Navier-Stokes (RANS) simulations of turbulent flows. The ABC method approximates posterior distributions of model parameters, but does not require the direct computation, or estimation, of a likelihood function. Compared to full Bayesian analyses, ABC thus provides a faster and more flexible parameter estimation for complex models and a wide range of reference data. In this paper, we describe the ABC approach, including the use of a calibration step, adaptive proposal, and Markov chain Monte Carlo (MCMC) technique to accelerate the parameter estimation, resulting in an improved ABC approach, denoted ABC-IMCMC. As a test of the classic ABC rejection algorithm, we estimate parameters in a nonequilibrium RANS model using reference data from direct numerical simulations of periodically sheared homogeneous turbulence. We then demonstrate the use of ABC-IMCMC to estimate parameters in the Menter shear-stress-transport (SST) model using experimental reference data for an axisymmetric transonic bump. We show that the accuracy of the SST model for this test case can be improved using ABC-IMCMC, indicating that ABC-IMCMC is a promising method for the calibration of RANS models using a wide range of reference data.