A Study of Large-eddy Simulation using Statistical and Machine Learning Techniques

Mohammed Khalid Hossen

doi:10.38032/jea.2022.03.004

Authors

Mohammed Khalid Hossen Department of Computer Science and Engineering, Sylhet Agricultural University, Sylhet, Bangladesh

DOI:

https://doi.org/10.38032/jea.2022.03.004

Keywords:

Navier-Stokes Equations, SGS Models, Vortex Stretching, Subgrid-scale Energy, Subgrid-scale Dissipation, Statistical and Machine Learning, Correlation, JPDF, Gradient Decent Algorithm

Abstract

The numerical solution of Navier-Stokes (N-S) equations has been found useful in various disciplines during its development, especially in recent years. However, a large-eddy simulation method has been developed to model the subgrid-scale dissipation rate by closing the Navier-Stokes equations. Because the instantaneous and time-averaged statistic characteristics of the subgrid-scale turbulent kinetic energy and dissipation have been studied by large eddy simulation. The purpose of this study is to check the statistical and machine learning of the subgrid-scale energy dissipation. As we know that the current turbulence theory states that the vortex stretching mechanism transports energy from large to small scales and leads to a high energy dissipation rate in a turbulent flow. Hence, a vortex-stretching-based subgrid-scale model is considered regarding the square of the velocity gradient to detect the playing role of the vortex stretching mechanism. The study in this article has shown a two-step process. Considering a posteriori statistic of the velocity gradient is analyzed through higher-order statistics and joint probability density function. Secondly, a machine learning approach is studied on the same data. The results of the vortex-stretching-based subgrid-scale model are then compared with the other two dynamic subgrid models, such as the localized dynamic kinetic energy equation model and the TKE-based Deardorff model. The results suggest that the vortex-stretching-based model can detect the significant subgrid-scale dissipation of small-scale motions and predict satisfactory turbulence statistics of the velocity gradient tensor.

References

Smagorinsky, J., 1963. General circulation experiments with the primitive equations: I. The basic experiment. Monthly Weather Review, 91(3), pp.99-164. DOI: https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

Taylor, G.I., 1938. Production and dissipation of vorticity in a turbulent fluid. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 164(916), pp.15-23. DOI: https://doi.org/10.1098/rspa.1938.0002

Carbone, M. and Bragg, A.D., 2020. Is vortex stretching the main cause of the turbulent energy cascade?. Journal of Fluid Mechanics, 883. DOI: https://doi.org/10.1017/jfm.2019.923

Sagaut, P. and Cambon, C., 2008. Homogeneous turbulence dynamics (Vol. 10). Cambridge: Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511546099

Pope, S.B. and Pope, S.B., 2000. Turbulent flows. Cambridge university press. DOI: https://doi.org/10.1017/CBO9780511840531

Nicoud, F. and Ducros, F., 1999. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, turbulence and Combustion, 62(3), pp.183-200.. DOI: https://doi.org/10.1023/A:1009995426001

Davidson, P. (2004). Turbulence: an introduction for scientists and engineers. Oxford University Press.

Hossen, M.K., Mulayath Variyath, A. and Alam, J.M., 2021. Statistical Analysis of Dynamic Subgrid Modeling Approaches in Large Eddy Simulation. Aerospace, 8(12), p.375. DOI: https://doi.org/10.3390/aerospace8120375

Kim, W.W. and Menon, S., 1995. A new dynamic one-equation subgrid-scale model for large eddy simulations. In 33rd Aerospace Sciences Meeting and Exhibit (p. 356). DOI: https://doi.org/10.2514/6.1995-356

Meneveau, C., 2010. Turbulence: Subgrid-scale modeling. Scholarpedia, 5(1), p.9489. DOI: https://doi.org/10.4249/scholarpedia.9489

Deardorff, J.W., 1972. Numerical investigation of neutral and unseq planetary boundary layers. Journal of Atmospheric Sciences, 29(1), pp.91-115. DOI: https://doi.org/10.1175/1520-0469(1972)029<0091:NIONAU>2.0.CO;2

Hossen, M. K., Variyath, A., & Alam, J., 2021. Statistical analysis of the role of vortex stretching in large eddy simulation. Proceedings of the 29th Annual Conference of the Computational Fluid Dynamics Society of Canada. CFDSC2021. July 27-29, Online.

Martın, J., Ooi, A., Chong, M.S. and Soria, J., 1998. Dynamics of the velocity gradient tensor invariants in isotropic turbulence. Physics of Fluids, 10(9), pp.2336-2346.

Jeong, J. and Hussain, F., 1995. On the identification of a vortex. Journal of Fluid Mechanics, 285, pp.69-94. DOI: https://doi.org/10.1017/S0022112095000462

Perry, A.E. and Chong, M.S., 1994. Topology of flow patterns in vortex motions and turbulence. Applied Scientific Research, 53(3), pp.357-374. DOI: https://doi.org/10.1007/BF00849110

Martın, J., Ooi, A., Chong, M.S. and Soria, J., 1998. Dynamics of the velocity gradient tensor invariants in isotropic turbulence. Physics of Fluids, 10(9), pp.2336-2346. DOI: https://doi.org/10.1063/1.869752

Dallas, V. and Alexakis, A., 2013. Structures and dynamics of small scales in decaying magnetohydrodynamic turbulence. Physics of Fluids, 25(10), p.105106. DOI: https://doi.org/10.1063/1.4824195

da Silva, C.B. and Pereira, J.C., 2008. Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Physics of Fluids, 20(5), p.055101. DOI: https://doi.org/10.1063/1.2912513

Hossen, M.K., 2022. Heart Disease Prediction Using Machine Learning Techniques. American Journal of Computer Science and Technology, 5(3), pp.146-154.

Wikipedia contributors. (2022, June 28). Gradient descent. In Wikipedia, The Free Encyclopedia. Retrieved 05:31, July 23, 2022, from https://en.wikipedia.org/w/index.php?title=Gradient_descent&oldid=1095507248.