Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning
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 <inline-formula>&l...
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2708 |
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| author | Konstantin Barkalov Ilya Lebedev Marina Usova Daria Romanova Daniil Ryazanov Sergei Strijhak |
| author_facet | Konstantin Barkalov Ilya Lebedev Marina Usova Daria Romanova Daniil Ryazanov Sergei Strijhak |
| author_sort | Konstantin Barkalov |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ω</mi><mspace width="4pt"></mspace><mi>S</mi><mi>S</mi><mi>T</mi></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-09T05:11:46Z |
| format | Article |
| id | doaj.art-2cd9eaf66cf544f7b1fb8f475d7dfc78 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:11:46Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2cd9eaf66cf544f7b1fb8f475d7dfc782023-12-03T12:48:08ZengMDPI AGMathematics2227-73902022-07-011015270810.3390/math10152708Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine LearningKonstantin Barkalov0Ilya Lebedev1Marina Usova2Daria Romanova3Daniil Ryazanov4Sergei Strijhak5Department of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, RussiaDepartment of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, RussiaDepartment of Mathematical Software and Supercomputing Technologies, Lobachevsky University, 603022 Nizhni Novgorod, RussiaIvannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, RussiaIvannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, RussiaIvannikov Institute for System Programming of the Russian Academy of Sciences, 109004 Moscow, RussiaThe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>−</mo><mi>ω</mi><mspace width="4pt"></mspace><mi>S</mi><mi>S</mi><mi>T</mi></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/10/15/2708global optimizationartificial neural networkfunction approximationfinite volume methodCFDOpenFOAM |
| spellingShingle | Konstantin Barkalov Ilya Lebedev Marina Usova Daria Romanova Daniil Ryazanov Sergei Strijhak Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning Mathematics global optimization artificial neural network function approximation finite volume method CFD OpenFOAM |
| title | Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning |
| title_full | Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning |
| title_fullStr | Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning |
| title_full_unstemmed | Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning |
| title_short | Optimization of Turbulence Model Parameters Using the Global Search Method Combined with Machine Learning |
| title_sort | optimization of turbulence model parameters using the global search method combined with machine learning |
| topic | global optimization artificial neural network function approximation finite volume method CFD OpenFOAM |
| url | https://www.mdpi.com/2227-7390/10/15/2708 |
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