Determining a priori a RANS model's applicable range via global epistemic uncertainty quantification

TL;DR

This paper introduces a global epistemic uncertainty quantification method to assess whether RANS model improvements will generalize beyond calibration data, using effectiveness and inconsistency metrics to predict applicability.

Contribution

The work presents a novel global epistemic UQ approach that evaluates the generalization potential of RANS model improvements through a quadrant-based effectiveness and inconsistency analysis.

Findings

The method successfully identified effective and consistent model coefficients for shear layer prediction.

Calibrated models in the high effectiveness, low inconsistency quadrant generalized well to other flow conditions.

Models with high inconsistency did not generalize beyond the calibration condition.

Abstract

Calibrating a Reynolds-averaged Navier-Stokes (RANS) model against data leads to an improvement. Determining {\it a priori} if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work attempts to address this challenge via global epistemic Uncertainty Quantification (UQ). Unlike the available epistemic UQ methods that are local and tell us a model's uncertainty at one specific flow condition, the global epistemic UQ method presented in this work tells us also whether a perturbation of the original model would generalize. Specifically, the global epistemic UQ method evaluates a potential improvement in terms of its "effectiveness" and "inconsistency". Any improvement can be put in one of the following four quadrants: first, high effectiveness, low inconsistency; second, high effectiveness, high inconsistency; third, low effectiveness, low inconsistency; and fourth, low effectiveness, high inconsistency. An improvement would generalize if and only if it is in the high effectiveness and low inconsistency quadrant. To demonstrate the concept, we apply the global epistemic UQ to full Reynolds stress modeling of a stratified shear layer. The global epistemic UQ results point to a model coefficient in the pressure-strain correlation closure (among others) as effective and consistent for predicting the quantity of interest of shear layer's growth. We calibrate the model coefficient such that our RANS matches direct numerical simulation data at one flow condition. We show that the calibrated model generalizes to several other test flow conditions. On the other hand, when calibrating a high inconsistency term, we get a model that works at only the calibrated condition.