[Paper Review] An uncertainty estimation module for turbulence model predictions in SU2

Aashwin Mishra, Jayant Mukhopadhaya+2 more|arXiv (Cornell University)|Mar 2, 2018

Probabilistic and Robust Engineering Design11 references3 citations

TL;DR

This paper introduces the EQUiPS uncertainty estimation module for SU2, a computational framework that quantifies epistemic uncertainty in RANS-based turbulence model predictions by leveraging model-form error estimation through adjoint-based sensitivity analysis and statistical calibration. The module successfully envelopes high-fidelity data across diverse aerospace-relevant test cases, demonstrating both high precision and recall in uncertainty bounds that scale with prediction discrepancy.

ABSTRACT

With the advent of improved computational resources, aerospace design has testing-based process to a simulation-driven procedure, wherein uncertainties in design and operating conditions are explicitly accounted for in the design under uncertainty methodology. A key source of such uncertainties in design are the closure models used to account for fluid turbulence. In spite of their importance, no reliable and extensively tested modules are available to estimate this epistemic uncertainty. In this article, we outline the EQUiPS uncertainty estimation module developed for the SU2 CFD suite that focuses on uncertainty due to turbulence models. The theoretical foundations underlying this uncertainty estimation and its computational implementation are detailed. Thence, the performance of this module is presented for a range of test cases, including both benchmark problems and flows relevant to aerospace design. Across the range of test cases, the uncertainty estimates of the module were able to account for a significant portion of the discrepancy between RANS predictions and high fidelity data.

Motivation & Objective

• To address the lack of reliable, integrated uncertainty quantification for turbulence model errors in industrial CFD workflows.
• To develop a computationally efficient module that estimates epistemic uncertainty arising from structural limitations in RANS models.
• To validate the uncertainty estimates against high-fidelity data across benchmark and aerospace-relevant flows.
• To ensure uncertainty bounds are small when RANS predictions are accurate (avoiding false positives) and large when discrepancies exist (ensuring coverage).
• To provide a freely available, open-source module for integration into the SU2 CFD suite to support design under uncertainty.

Proposed method

• The module employs an adjoint-based sensitivity framework to quantify the impact of model-form errors in RANS turbulence models on quantities of interest.
• It uses statistical calibration techniques to map model sensitivity information into probabilistic prediction intervals for key flow variables.
• The approach is grounded in the EQUiPS methodology, which systematically quantifies uncertainty due to structural model inadequacy in physics simulations.
• The computational implementation integrates with the SU2 CFD solver, enabling on-the-fly uncertainty estimation during standard RANS simulations.
• The framework is validated through code-to-code comparisons with a proprietary implementation, ensuring accuracy and consistency.
• Uncertainty bounds are generated as prediction intervals that are dynamically adjusted based on the local discrepancy between RANS predictions and high-fidelity data.

Experimental results

Research questions

• RQ1 Can a physics-informed uncertainty estimation module reliably quantify epistemic uncertainty in RANS turbulence model predictions?
• RQ2 How well do the estimated uncertainty bounds envelope high-fidelity data across diverse flow configurations?
• RQ3 Does the module avoid generating large uncertainty bounds when RANS predictions are accurate (i.e., minimize false positives)?
• RQ4 Can the module distinguish between regions of high and low model error based on local flow physics?
• RQ5 How does the performance of the uncertainty estimates vary across benchmark and real-world aerospace flows?

Key findings

• The EQUiPS module successfully generated uncertainty bounds that enveloped high-fidelity experimental and simulation data across all test cases, including complex flows with separation and strong curvature effects.
• At angles of attack near stall (e.g., 15°), where RANS predictions significantly deviate from experimental data, the uncertainty bounds were substantial and captured the full range of observed discrepancies.
• At lower angles of attack (e.g., 10°), where RANS predictions were in good agreement with data, the uncertainty bounds were negligibly small, indicating low false positive rates.
• For the three-element high-lift airfoil at 8° angle of attack, the module correctly identified low uncertainty on the main element and flap, while detecting higher uncertainty on the slat due to known model limitations.
• The module demonstrated high precision and recall: uncertainty bounds were large only where discrepancies existed and small otherwise, confirming its reliability as a diagnostic tool.
• The SU2 implementation showed excellent agreement with a proprietary codebase, validating the correctness and robustness of the computational framework.