Non-linear structure-based modeling of the rapid pressure strain rate correlation using machine learning

Modeling the rapid pressure strain rate (RPSR) correlation in the Reynolds Stress Transport Equations is a fundamental challenge for developing Reynolds Stress closures in Reynolds Averaged Navier Stokes (RANS) simulations. Earlier attempts have seen limited success, which is hypothesized to be due to missing model dependencies. Kassinos et al. [1] proposed using an extended set of dependencies consisting of the dimensionality and stropholysis structure tensors in addition to the Reynolds stress, and derived a linear model for the RPSR correlation in terms of them, which still exhibited deficiencies. In this work, new nonlinear closure models are developed in terms of the structure tensors. The coefficients appearing in the models are learned as a function of the structure tensor invariants using machine learning trained on a broad ensemble of rapidly distorted turbulence (RDT) simulations. An in-depth analysis of the original linear model and the new nonlinear models is carried out. This development is the first step towards showing that the structure tensors provide a sufficiently rich statistical description of turbulence to enable the modeling of complex turbulent flows.

[1]. Kassinos, S. C., Reynolds, W. C., & Rogers, M. M. (2001). One-point turbulence structure tensors. Journal of Fluid Mechanics, 428, 213-248.