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.