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. Furthermore, 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.
Ling, Julia, et al. "Reynolds averaged turbulence modelling using deep neural networks with embedded invariance." Journal of Fluid Mechanics, vol. 807, Oct. 2016. https://doi.org/10.1017/jfm.2016.615
Ling, Julia, Kurzawski, Andrew, & Templeton, Jeremy (2016). Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. Journal of Fluid Mechanics, 807. https://doi.org/10.1017/jfm.2016.615
Ling, Julia, Kurzawski, Andrew, and Templeton, Jeremy, "Reynolds averaged turbulence modelling using deep neural networks with embedded invariance," Journal of Fluid Mechanics 807 (2016), https://doi.org/10.1017/jfm.2016.615
@article{osti_1333570,
author = {Ling, Julia and Kurzawski, Andrew and Templeton, Jeremy},
title = {Reynolds averaged turbulence modelling using deep neural networks with embedded invariance},
annote = {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. Furthermore, 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.},
doi = {10.1017/jfm.2016.615},
url = {https://www.osti.gov/biblio/1333570},
journal = {Journal of Fluid Mechanics},
issn = {ISSN 0022-1120},
volume = {807},
place = {United States},
publisher = {Cambridge University Press},
year = {2016},
month = {10}}
Bode, Mathis; Gauding, Michael; Kleinheinz, Konstantin
High Performance Computing: ISC High Performance 2019 International Workshops, Frankfurt, Germany, June 16-20, 2019, Revised Selected Papers, p. 541-560https://doi.org/10.1007/978-3-030-34356-9_41
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