Customized data-driven RANS closures for bi-fidelity LES–RANS optimization

Yu Zhang, Richard P. Dwight*, Martin Schmelzer, Javier F. Gómez, Zhong hua Han, Stefan Hickel

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
45 Downloads (Pure)


Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low- and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high- and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES–RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES–RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectivity and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.

Original languageEnglish
Article number110153
JournalJournal of Computational Physics
Publication statusPublished - 2021


  • Algebraic stress model
  • Large-eddy simulation
  • Multi-fidelity optimization
  • Reynolds-averaged Navier-Stokes
  • Turbulence modelling


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