Parameter Estimation for RANS Models Using Approximate Bayesian Computation

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.

Invariant Data-Driven Subgrid Stress Modeling in the Strain-Rate Eigenframe for Large Eddy Simulation

“…If one utilizes the minimal integrity basis of polynomial invariants as a set of model inputs and the expansion coefficients as a set of model outputs, one arrives at a rotationally and reflectionally invariant model form. While this strategy has been employed for both datadriven Reynolds stress closure modeling [16,17] and data-driven SGS closure modeling [15,34,35], it suffers from the issue that sizes of the minimal tensor and invariant integrity bases grow exponentially fast with the number of prescribed tensor inputs. A second strategy is to model the eigenstructure of the SGS tensor, that is, its eigenvalues and eigenvectors, as functions of invariant model inputs.…”

Bayesian Calibration With Adaptive Model Discrepancy

“…Their Bayesian framework represents the model discrepancy with Gaussian processes. It has been widely applied in various fields such as aerodynamics [4][5][6][7], fluid mechanics [8,9] and solid mechanics ( [10,11]). Compared to standard calibration, inferring the model discrepancy jointly with the parameters yields more objective and less informative parameter posteriors.…”