Data-driven nonlinear K-L turbulent mixing model via gene expression programming method.

Reynolds-averaged Navier-Stokes (RANS) simulation is currently the primary approach for engineering predictions of turbulent mixing induced by Rayleigh-Taylor (RT), Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities. However, traditional Boussinesq-type RANS mixing models are inadequate for resolving turbulence anisotropy that plays an important role in most of engineering flows. In this study, a data-driven nonlinear K-L mixing model is developed via the gene expression programming (GEP) method to provide an explicit and interpretable model, which can be easily ported to different RANS solvers. Specifically, the Reynolds stress is closed with a second-order truncated generalized Cayley-Hamilton constitutive relation, where the undetermined coefficients are expressed as functions of the Galilean invariants and are trained by the GEP method. Additionally, the realizability principle is considered in the cost function to ensure physics of the flow field. The results of a series of tests confirm that the new model is robust with different mixing problems, though the training is conducted only with the tilted RT mixing problem. When compared with the baseline K-L model, the new model not only significantly improves the predictive accuracy, but also captures physics of turbulence at a higher level. As the model has been explicitly expressed, the improvements are further interpreted by analyzing the equations. To the best of our knowledge, this is the first study to investigate turbulent mixing problems using machine learning methods. [ABSTRACT FROM AUTHOR]