Liutex based data-driven turbulence model correction

The current widely used turbulence models often exhibit significant discrepancies with experimental results for largely separated flows primarily due to the strong adverse pressure gradients present in the flows, which violate the fundamental assumptions of turbulence models. To enhance the computational accuracy for largely separated flow problems, it is necessary to modify the turbulence models. A combined approach of field inversion and data-driven methods is proposed to introduce a neural network for the correction of the Spalart-Allmaras (S-A) one-equation model based on Liutex. Initially, correction coefficients for the S-A one-equation model generation terms are obtained through field inversion with discrete adjoint. Feature selection indicates that Liutex exhibits the highest correlation with the correction coefficients for the S-A one-equation model generation terms and is suitable as an input for the neural network. Subsequently, Liutex and other variables are used as inputs to construct a neural network to approximate the correction coefficients for the S-A model generation terms, establishing the neural network structure for the generation term correction coefficients. This correction method is validated through separated flow results for the S809 and S814 airfoils, demonstrating the ability to significantly improve the computational accuracy of largely separated flows.