Efficient prediction of turbulent flow quantities using a Bayesian hierarchical multifidelity model

• Main Authors: Rezaeiravesh, Saleh, Mukha, Timofey, Schlatter, Philipp
• Format: Journal Article
• Language: English
• Published: 26-10-2022
• Subjects: Physics - Fluid Dynamics
• DOI: 10.48550/arxiv.2210.14790

High-fidelity scale-resolving simulations of turbulent flows quickly become
prohibitively expensive, especially at high Reynolds numbers. As a remedy, we
may use multifidelity models (MFM) to construct predictive models for flow
quantities of interest (QoIs), with the purpose of uncertainty quantification,
data fusion and optimization. For numerical simulation of turbulence, there is
a hierarchy of methodologies ranked by accuracy and cost, which include several
numerical/modeling parameters that control the predictive accuracy and
robustness of the resulting outputs. Compatible with these specifications, the
present hierarchical MFM strategy allows for simultaneous calibration of the
fidelity-specific parameters in a Bayesian framework as developed by Goh et al.
2013. The purpose of the multifidelity model is to provide an improved
prediction by combining lower and higher fidelity data in an optimal way for
any number of fidelity levels; even providing confidence intervals for the
resulting QoI. The capabilities of our multifidelity model are first
demonstrated on an illustrative toy problem, and it is then applied to three
realistic cases relevant to engineering turbulent flows. The latter include the
prediction of friction at different Reynolds numbers in turbulent channel flow,
the prediction of aerodynamic coefficients for a range of angles of attack of a
standard airfoil, and the uncertainty propagation and sensitivity analysis of
the separation bubble in the turbulent flow over periodic hills subject to the
geometrical uncertainties. In all cases, based on only a few high-fidelity data
samples (typically direct numerical simulations, DNS), the multifidelity model
leads to accurate predictions of the QoIs accompanied with an estimate of
confidence. The result of the UQ and sensitivity analyses are also found to be
accurate compared to the ground truth in each case.