A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations

doi:10.1007/s10483-023-3028-9

Applied Mathematics and Mechanics (English Edition) ›› 2023, Vol. 44 ›› Issue (9): 1597-1612.doi: https://doi.org/10.1007/s10483-023-3028-9

A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations

Haoyang LI¹, Weijian LIU¹, Yuhong DONG^1,2,3,4

1. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China;
2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
3. Shanghai Frontier Science Center of Mechanoinformatics, Shanghai University, Shanghai 200072, China;
4. Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China

收稿日期:2023-03-22 修回日期:2023-06-30 发布日期:2023-08-28
通讯作者: Yuhong DONG, E-mail: dongyh@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos.12172207 and 92052201)

A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations

Haoyang LI¹, Weijian LIU¹, Yuhong DONG^1,2,3,4

1. Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China;
2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
3. Shanghai Frontier Science Center of Mechanoinformatics, Shanghai University, Shanghai 200072, China;
4. Shanghai Institute of Aircraft Mechanics and Control, Shanghai 200092, China

Received:2023-03-22 Revised:2023-06-30 Published:2023-08-28
Contact: Yuhong DONG, E-mail: dongyh@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.12172207 and 92052201)

摘要/Abstract

摘要： Understanding and modeling flows over porous layers are of great industrial significance. To accurately solve the turbulent multi-scale flows on complex configurations, a rescaling algorithm designed for turbulent flows with the Chapman-Enskog analysis is proposed. The mesh layout and the detailed rescaling procedure are also introduced. Direct numerical simulations (DNSs) for a turbulent channel flow and a porous walled turbulent channel flow are performed with the three-dimensional nineteen-velocity (D3Q19) multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) to validate the accuracy, adaptability, and computational performance of the present rescaling algorithm. The results, which are consistent with the previous DNS studies based on the finite difference method and the LBM, demonstrate that the present method can maintain the continuity of the macro values across the grid interface and is able to adapt to complex geometries. The reasonable time consumption of the rescaling procedure shows that the present method can accurately calculate various turbulent flows with multi-scale and complex configurations while maintaining high computational efficiency.

关键词: lattice Boltzmann method (LBM), direct numerical simulation (DNS), rescaling algorithm, complex configuration

Abstract: Understanding and modeling flows over porous layers are of great industrial significance. To accurately solve the turbulent multi-scale flows on complex configurations, a rescaling algorithm designed for turbulent flows with the Chapman-Enskog analysis is proposed. The mesh layout and the detailed rescaling procedure are also introduced. Direct numerical simulations (DNSs) for a turbulent channel flow and a porous walled turbulent channel flow are performed with the three-dimensional nineteen-velocity (D3Q19) multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) to validate the accuracy, adaptability, and computational performance of the present rescaling algorithm. The results, which are consistent with the previous DNS studies based on the finite difference method and the LBM, demonstrate that the present method can maintain the continuity of the macro values across the grid interface and is able to adapt to complex geometries. The reasonable time consumption of the rescaling procedure shows that the present method can accurately calculate various turbulent flows with multi-scale and complex configurations while maintaining high computational efficiency.

Key words: lattice Boltzmann method (LBM), direct numerical simulation (DNS), rescaling algorithm, complex configuration

中图分类号:

76M28

Haoyang LI, Weijian LIU, Yuhong DONG. A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1597-1612.

参考文献

[1] CHEN, S. and DOOLEN, G. D. Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 30(1), 329-364(1998)
[2] OBRECHT, C., KUZNIK, F., TOURANCHEAU, B., and ROUX, J. J. Multi-GPU implementation of the lattice Boltzmann method. Computers & Mathematics with Applications, 65(2), 252-261(2013)
[3] KRÜGER, T., KUSUMAATMAJA, H., KUZMIN, A., SHARDT, O., SILVA, G., and VIGGEN, E. M. The Lattice Boltzmann Method, Springer, Cham, 4-15(2017)
[4] EGGELS, J. G. Direct and large-eddy simulation of turbulent fluid flow using the lattice-Boltzmann scheme. International Journal of Heat and Fluid Flow, 17(3), 307-323(1996)
[5] JAHANSHALOO, L., POURYAZDANPANAH, E., and CHE SIDIK, N. A. A review on the application of the lattice Boltzmann method for turbulent flow simulation. Numerical Heat Transfer, Part A: Applications, 64(11), 938-953(2013)
[6] AIDUN, C. K. and CLAUSEN, J. R. Lattice-Boltzmann method for complex flows. Annual Review of Fluid Mechanics, 42, 439-472(2010)
[7] LIU, H., KANG, Q., LEONARDI, C. R., SCHMIESCHEK, S., NARVÁEZ, A., JONES, B. D., WILLIAMS, J. R., VALOCCHI, A. J., and HARTING, J. Multiphase lattice Boltzmann simulations for porous media applications. Computational Geosciences, 20(4), 777-805(2016)
[8] YANG, F. C. and CHEN, X. P. Numerical simulation of two-dimensional viscous flows using combined finite element-immersed boundary method. Journal of Hydrodynamics, 27(5), 658-667(2015)
[9] LI, Q. X., PAN, M., and DONG, Y. H. Turbulence modulation and heat transfer enhancement in channels roughened by cube-covered surface. Computers & Fluids, 165, 33-42(2018)
[10] LI, Q. X., PAN, M., ZHOU, Q., and DONG, Y. H. Turbulent drag reduction by spanwise oscillations of a channel wall with porous layer. Computers & Fluids, 180, 1-10(2019)
[11] HUANG, R. and WU, H. Multiblock approach for the passive scalar thermal lattice Boltzmann method. Physical Review E, 89(4), 043303(2014)
[12] KARANI, H. and HUBER, C. Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media. Physical Review E, 91(2), 023304(2015)
[13] PAN, M., LI, Q., TANG, S., and DONG, Y. H. Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method. Applied Mathematics and Mechanics (English Edition), 39(4), 477-488(2018) https://doi.org/10.1007/s10483-018-2316-8
[14] FILIPPOVA, O. and HÄNEL, D. Grid refinement for lattice-BGK models. Journal of Computational Physics, 147(1), 219-228(1998)
[15] YU, D., MEI, R., and SHYY, W. A multi-block lattice Boltzmann method for viscous fluid flows. International Journal for Numerical Methods in Fluids, 39(2), 99-120(2002)
[16] DUPUIS, A. and CHOPARD, B. Theory and applications of an alternative lattice Boltzmann grid refinement algorithm. Physical Review E, 67(6), 066707(2003)
[17] BHATNAGAR, P. L., GROSS, E. P., and KROOK, M. A model for collision processes in gases, I, small amplitude processes in charged and neutral one-component systems. Physical Review, 94(3), 511(1954)
[18] KUWATA, Y. and SUGA, K. Imbalance-correction grid-refinement method for lattice Boltzmann flow simulations. Journal of Computational Physics, 311, 348-362(2016)
[19] WU, C. M., ZHOU, Y. S., and LIN, C. A. Direct numerical simulations of turbulent channel flows with mesh-refinement lattice Boltzmann methods on GPU cluster. Computers & Fluids, 210, 104647(2020)
[20] D'HUMIÈRES, D. Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 360(1792), 437-451(2002)
[21] TANG, Z., LIU, N. S., and DONG, Y. H. Lattice Boltzmann simulations of turbulent shear flow between parallel porous walls. Applied Mathematics and Mechanics (English Edition), 35(12), 1479-1494(2014) https://doi.org/10.1007/s10483-014-1885-6
[22] LIU, Z., LI, S., RUAN, J., ZHANG, W. B., ZHOU, L. P., HUANG, D. M., and XU, J. X. A new multi-level grid multiple-relaxation-time lattice Boltzmann method with spatial interpolation. Mathematics, 11(5), 1089(2023)
[23] LAGRAVA, D., MALASPINAS, O., LATT, J., and CHOPARD, B. Advances in multi-domain lattice Boltzmann grid refinement. Journal of Computational Physics, 231(14), 4808-4822(2012)
[24] LALLEMAND, P. and LUO, L. S. Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Physical Review E, 61(6), 6546(2000)
[25] GUO, Z., ZHENG, C., and SHI, B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E, 65(4), 046308(2002)
[26] KIM, J., MOIN, P., and MOSER, R. Turbulence statistics in fully developed channel flow at low Reynolds number. Journal of Fluid Mechanics, 177, 133-166(1987)
[27] KUWATA, Y. and SUGA, K. Direct numerical simulation of turbulence over anisotropic porous media. Journal of Fluid Mechanics, 831, 41-71(2017)
[28] BREUGEM, W., BOERSMA, B., and UITTENBOGAARD, R. The influence of wall permeability on turbulent channel flow. Journal of Fluid Mechanics, 562, 35-72(2006)
[29] CHIKATAMARLA, S. S., FROUZAKIS, C. E., KARLIN, I. V., TOMBOULIDES, A. G., and BOULOUCHOS, K. B. Lattice Boltzmann method for direct numerical simulation of turbulent flows. Journal of Fluid Mechanics, 656, 298-308(2010)
[30] BESPALKO, D., POLLARD, A., and UDDIN, M. Analysis of the pressure fluctuations from an LBM simulation of turbulent channel flow. Computers & Fluids, 54, 143-146(2012)
[31] SUGA, K., OKAZAKI, Y., MATSUO, T., TANEO, A., and KUWATA, T. Measurement of turbulent square duct flows over anisotropic porous media. 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Begel House Inc., Southampton (2019)

A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations

A rescaling algorithm for multi-relaxation-time lattice Boltzmann method towards turbulent flows with complex configurations

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