S-frame discrepancy correction models for data-informed Reynolds stress closure

Despite their well-known limitations, Reynolds averaged Navier-Stokes (RANS) models remain the most commonly employed tool for modeling turbulent flows in engineering practice. RANS models are predicated on the solution of the RANS equations, but the RANS equations involve an unclosed term, the Reynolds stress tensor, which must be modeled. The Reynolds stress tensor is often modeled as an algebraic function of mean flow field variables and turbulence variables. This, however, introduces a discrepancy between the Reynolds stress tensor predicted by the Reynolds stress model and the exact Reynolds stress tensor. This discrepancy can result in inaccurate mean flow field predictions for complex flows of industrial relevance. In this paper, we introduce a data-informed approach for arriving at Reynolds stress models with improved predictive performance. Our approach relies on learning the components of the Reynolds stress discrepancy tensor associated with a given Reynolds stress model in the mean strain-rate tensor eigenframe. These components are typically smooth and hence simple to learn using state-of-the-art machine learning strategies and regression techniques. Our approach automatically yields Reynolds stress models that are symmetric, and it yields Reynolds stress models that are both Galilean and frame invariant provided the inputs are themselves Galilean and frame invariant. To arrive at computable models of the discrepancy tensor, we employ feed forward neural networks and an input space spanning the integrity basis of the mean strain-rate tensor, the mean rotation-rate tensor, the mean pressure gradient, and the turbulent kinetic energy gradient, and we introduce a framework for dimensional reduction of the input space to further reduce computational cost. Numerical results illustrate the effectiveness of the proposed approach for data-informed Reynolds stress closure for a suite of turbulent flow problems of increasing complexity. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

Despite their limitations, Reynolds averaged Navier-Stokes (RANS) models are still widely used in engineering practice for modeling turbulent flows. This paper introduces a data-informed approach for improving the predictive performance of Reynolds stress models by learning components of the Reynolds stress discrepancy tensor. The proposed approach automatically generates symmetric Reynolds stress models that are Galilean and frame invariant, showing effectiveness in various turbulent flow problems.