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Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

Published online by Cambridge University Press:  18 October 2016

Julia Ling ,
Andrew Kurzawski  and
Jeremy Templeton
Julia Ling*
Affiliation:
Thermal/Fluids Science and Engineering Department, Sandia National Labs, Livermore, CA 94550, USA
Andrew Kurzawski
Affiliation:
Mechanical Engineering Department, University of Texas at Austin, Austin, TX 78712, USA
Jeremy Templeton
Affiliation:
Thermal/Fluids Science and Engineering Department, Sandia National Labs, Livermore, CA 94550, USA
*
†Email address for correspondence: jling@sandia.gov
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Abstract

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 155 - 166
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Copyright
© Cambridge University Press 2016. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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