Tuning of Turbulence Model Closure Coefficients Using an Explainability Based Machine Learning Algorithm

This article discusses an application of Machine Learning (ML) tools to improve the prediction accuracy of Computational Fluid Dynamics (CFD) for external aerodynamic workflows. The Reynolds Averaged Navier-Stokes (RANS) approach to CFD has proved to be one of the most popular simulation methodologies due to its quick turnaround times and acceptable level of accuracy for most applications. However, in many cases the accuracy for the RANS models can prove to be suboptimal that can be significantly improved with model closure coefficient tuning. During the original turbulence model creation, these closure coefficients were chosen by somewhat ad hoc methods using simple canonical flows that do not transfer well to flows involving more complex objects, like the automotive bodies used in this work. This work presents a novel method of applying ML tools to CFD to optimize the turbulence closure coefficients by using model explainability tools such as Shapley Values, Shapley Additive exPlanations (SHAP), and ML surrogate models. The 25-degree slant Ahmed body model was used to obtain sampling data to tune closure coefficient in the Menter Shear Stress Transport (SST) turbulence model implemented in the open source CFD code, OpenFOAM v2012. Shapley additive values were then calculated using the samples which showed that β^∗ has the strongest influence over the model predictions of lift and drag. ML surrogate models were then applied alongside SHAP providing a better overall sampling efficiency with Shapley additive values and more complete explanations of the model. The SHAP explanations showed that β^∗ had the most influence on the force predictions followed by σ_ω2, while σ_ω1, σ_k1, and σ_k2 were shown to have little impact. The surrogate model was then used along with its explanations to provide optimized coefficients that reduced the error in the drag and lift predictions to -3.67% and -2.49% respectively, from -9.67% and -75.8%.