A review of pressure strain correlation modeling for Reynolds stress models

Most investigations of turbulent flows in academic studies and industrial applications use turbulence models. Out of the different turbulence modeling approaches Reynolds stress models have the highest potential to replicate complex turbulent flow phenomena at a reasonable computational expense. The Reynolds stress modeling framework is constituted by individual closures that approximate the effects of separate turbulence processes like dissipation, turbulent transport, pressure strain correlation, etc. Owing to its complexity and importance in flow evolution the modeling of the pressure strain correlation mechanism is considered the crucial challenge for the Reynolds stress modeling framework. In the present work, the modeling of the pressure strain correlation for homogeneous turbulent flows is reviewed. The importance of the pressure strain correlation and its effects on flow evolution via energy transfer are established. The fundamental challenges in pressure stain correlation modeling are analyzed and discussed. Starting from the governing equations we outline the theory behind models for both the slow and rapid pressure strain correlation. Established models for both these are introduced and their successes and shortcomings are illustrated using theoretical analysis, computational fluid dynamics simulations, and comparisons against experimental and numerical studies. Recent advances and developments in this field are presented and discussed. The application of machine learning algorithms such as Deep Neural Networks, Random Forests, and Gradient Boosted Regression Trees is summarized and examined. We report fundamental problems in the application of machine learning algorithms for pressure strain correlation modeling. Finally, challenges and hurdles for pressure strain correlation modeling are outlined and explained in detail to guide future investigations.