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Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning

Author

Listed:
  • Konstantin Barkalov

    (Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, Russia)

  • Ilya Lebedev

    (Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, Russia)

  • Marina Usova

    (Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, Russia)

  • Daria Romanova

    (Ivannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia
    Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia)

  • Daniil Ryazanov

    (Ivannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia)

  • Sergei Strijhak

    (Ivannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, Russia
    Moscow Aviation Institute, Volokolamskoe Shosse 4, 125993 Moscow, Russia)

Abstract

The paper considers the slope flow simulation and the problem of finding the optimal parameter values of this mathematical model. The slope flow is modeled using the finite volume method applied to the Reynolds-averaged Navier–Stokes equations with closure in the form of the k − ω S S T turbulence model. The optimal values of the turbulence model coefficients for free surface gravity multiphase flows were found using the global search algorithm. Calibration was performed to increase the similarity of the experimental and calculated velocity profiles. The Root Mean Square Error (RMSE) of derivation between the calculated flow velocity profile and the experimental one is considered as the objective function in the optimization problem. The calibration of the turbulence model coefficients for calculating the free surface flows on test slopes using the multiphase model for interphase tracking has not been performed previously. To solve the multi-extremal optimization problem arising from the search for the minimum of the loss function for the flow velocity profile, we apply a new optimization approach using a Peano curve to reduce the dimensionality of the problem. To speed up the optimization procedure, the objective function was approximated using an artificial neural network. Thus, an interdisciplinary approach was applied which allowed the optimal values of six turbulence model parameters to be found using OpenFOAM and Globalizer software.

Suggested Citation

  • Konstantin Barkalov & Ilya Lebedev & Marina Usova & Daria Romanova & Daniil Ryazanov & Sergei Strijhak, 2022. "Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2708-:d:876956
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    References listed on IDEAS

    as
    1. Rommel Regis & Christine Shoemaker, 2005. "Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions," Journal of Global Optimization, Springer, vol. 31(1), pages 153-171, January.
    2. Cheung, Sai Hung & Oliver, Todd A. & Prudencio, Ernesto E. & Prudhomme, Serge & Moser, Robert D., 2011. "Bayesian uncertainty analysis with applications to turbulence modeling," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1137-1149.
    3. Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2018. "Metaheuristic vs. deterministic global optimization algorithms: The univariate case," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 245-259.
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