Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions. Existing approaches often struggle with generalization beyond training cases and lack robust uncertainty quantification frameworks, limiting their utility in complex flow regimes. We propose a Bayesian neural network (BNN)-based framework specifically designed for two-dimensional separated flows. By focusing on flow zones near separated regions, we ensure targeted training and enhance predictive reliability. The BNN framework incorporates physics-guided, invariant inputs to maintain consistency with turbulence physics. Correction terms predicted by the BNN are selectively applied to specific regions of the flow domain using a novel classifier, improving accuracy. A key feature of this approach is propagating BNN-derived corrections to flow solutions, enabling uncertainty quantification in unseen test cases. This probabilistic characterization of modeling errors offers insights into the reliability of RANS predictions across geometries with similar topologies. Preliminary results demonstrate that this method accurately predicts correction terms for Reynolds stress anisotropy and turbulent kinetic energy production in separated flow regions, effectively addressing dominant modeling errors and advancing turbulence modeling through uncertainty quantification.

This thesis explores the use of Bayesian Deep Learning to improve uncertainty quantification in Reynolds-Averaged Navier-Stokes (RANS) turbulence models. While RANS models are commonly used in computational fluid dynamics due to their efficiency, they are often criticized for inaccuracies in certain flow conditions, primarily due to the challenges in modeling the Reynolds stress term. The thesis acknowledges the limitations of traditional turbulence models, which rely heavily on empirical parameters and often fail to generalize across different flow scenarios, leading to significant uncertainties.

To address these issues, the research introduces a data-driven approach, leveraging Bayesian Neural Networks (BNNs). BNNs are particularly suitable for this task because they not only improve prediction accuracy but also provide a mechanism to quantify uncertainties arising from both the model and the data. This dual uncertainty quantification is critical, as it helps to address the inherent ”black box” nature of machine learning models, which can introduce additional uncertainties into the predictions.

The methodology involves correcting traditional turbulence models and integrating them with BNNs to capture both aleatoric (data-driven) and epistemic (model-driven) uncertainties. The thesis demonstrates the effectiveness of this approach through various flow case studies, comparing the results against more accurate but computationally expensive methods like Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS).

The research concludes that the integration of Bayesian Neural Networks into RANS turbulence models not only enhances predictive accuracy but also provides a more comprehensive uncertainty quantification, making it a promising direction for future work in turbulence modeling.