On developing data-driven turbulence model for DG solution of RANS

High-order Discontinuous Galerkin (DG) methods have been receiving more and more attentions in the area of Computational Fluid Dynamics (CFD) because of their high-accuracy property. However, it is still a challenge to obtain converged solution rapidly when solving the Reynolds Averaged Navier–Stokes (RANS) equations since the turbulence models significantly increase the nonlinearity of discretization system. The overall goal of this research is to develop an Artificial Neural Networks (ANNs) model with low complexity acting as an algebraic turbulence model to estimate the turbulence eddy viscosity for RANS. The ANN turbulence model is off-line trained using the training data generated by the widely used Spalart–Allmaras (SA) turbulence model before the Optimal Brain Surgeon (OBS) is employed to determine the relevancy of input features. Using the selected relevant features, a fully connected ANN model is constructed. The performance of the developed ANN model is numerically tested in the framework of DG for RANS, where the “DG+ANN” method provides robust and steady convergence compared to the “DG+SA” method. The results demonstrate the promising potential to develop a general turbulence model based on artificial intelligence in the future given the training data covering a large rang of flow conditions.