Development and Comparative Studies of Three Non-Free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

Development and Comparative Studies of Three Non-Free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows

Year:    2012

Author:    L. M. Yang, C. Shu, J. Wu

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 454–472

Abstract

This paper at first shows the details of finite volume-based lattice Boltzmann method (FV-LBM) for simulation of compressible flows with shock waves. In the FV-LBM, the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model, while the tangential flux is calculated using the same way as used in the conventional Euler solvers. The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM. The platform is formed from the conservation forms of moments. Under the platform, both the equilibrium distribution functions and lattice velocities can be determined, and therefore, non-free parameter model can be developed. The paper particularly presents three typical non-free parameter models, D1Q3, D1Q4 and D1Q5. The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems. Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number. From the results, it seems that D1Q4 model could be the best choice for the FV-LBM simulation of hypersonic flows.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m11146

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 4 : pp. 454–472

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    FV-LBM non-free parameter models compressible inviscid flows.

Author Details

L. M. Yang

C. Shu

J. Wu

  1. Effects of rough elements in fractures on seepage law based on lattice Boltzmann method

    Cai, Meng | Yang, Liu | Tan, Fengqi | Wang, Suling | Wu, Yonghong

    Desalination and Water Treatment, Vol. 319 (2024), Iss. P.100520

    https://doi.org/10.1016/j.dwt.2024.100520 [Citations: 0]
  2. A high-order scheme based on lattice Boltzmann flux solver for viscous compressible flow simulations

    Qin, Jian | Wu, Jie | Ma, Chao

    Applied Mathematics and Mechanics, Vol. 43 (2022), Iss. 10 P.1601

    https://doi.org/10.1007/s10483-022-2913-7 [Citations: 0]
  3. Linear discrete velocity model-based lattice Boltzmann flux solver for simulating acoustic propagation in fluids

    Zhan, Ningyu | Chen, Rongqian | Song, Qiaochu | You, Yancheng

    Physical Review E, Vol. 105 (2022), Iss. 6

    https://doi.org/10.1103/PhysRevE.105.065303 [Citations: 4]
  4. Lattice Boltzmann method for compressible Euler equations based on exact kinetic system

    Hanada, Takaya | Kataoka, Takeshi

    International Journal for Numerical Methods in Fluids, Vol. 93 (2021), Iss. 8 P.2554

    https://doi.org/10.1002/fld.4987 [Citations: 2]
  5. Development of lattice Boltzmann flux solver for simulation of hypersonic flow past flight vehicles

    Meng, Zhuxuan | Yang, Liming | Shu, Chang | Hu, Fan | Wang, Donghui | Zhang, Weihua

    Journal of Physics: Conference Series, Vol. 1053 (2018), Iss. P.012073

    https://doi.org/10.1088/1742-6596/1053/1/012073 [Citations: 0]
  6. Circular function-based gas-kinetic scheme for simulation of inviscid compressible flows

    Yang, L.M. | Shu, C. | Wu, J. | Zhao, N. | Lu, Z.L.

    Journal of Computational Physics, Vol. 255 (2013), Iss. P.540

    https://doi.org/10.1016/j.jcp.2013.08.025 [Citations: 45]
  7. A rotating reference frame‐based lattice Boltzmann flux solver for simulation of turbomachinery flows

    Zhou, Di | Lu, Zhiliang | Guo, Tongqing

    International Journal for Numerical Methods in Fluids, Vol. 83 (2017), Iss. 7 P.561

    https://doi.org/10.1002/fld.4281 [Citations: 12]
  8. A moment conservation-based non-free parameter compressible lattice Boltzmann model and its application for flux evaluation at cell interface

    Yang, L.M. | Shu, C. | Wu, J.

    Computers & Fluids, Vol. 79 (2013), Iss. P.190

    https://doi.org/10.1016/j.compfluid.2013.03.020 [Citations: 40]
  9. A modified lattice Boltzmann approach based on radial basis function approximation for the non‐uniform rectangular mesh

    Hu, X. | Bergadà, J. M. | Li, D. | Sang, W. M. | An, B.

    International Journal for Numerical Methods in Fluids, Vol. 96 (2024), Iss. 11 P.1695

    https://doi.org/10.1002/fld.5318 [Citations: 0]
  10. A spectral difference lattice Boltzmann method for solution of inviscid compressible flows on structured grids

    Hejranfar, Kazem | Ghaffarian, Ali

    Computers & Mathematics with Applications, Vol. 72 (2016), Iss. 5 P.1341

    https://doi.org/10.1016/j.camwa.2016.06.043 [Citations: 12]
  11. Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows

    Wang, Y. | Shu, C. | Teo, C.J.

    Computers & Fluids, Vol. 94 (2014), Iss. P.98

    https://doi.org/10.1016/j.compfluid.2014.02.006 [Citations: 84]
  12. A combined flux reconstruction and lattice Boltzmann flux solver for inviscid compressible flow simulation

    Qin, Jian | Wu, Jie | Gu, Xiangyu | Ma, Chao

    International Journal for Numerical Methods in Fluids, Vol. 94 (2022), Iss. 12 P.2087

    https://doi.org/10.1002/fld.5137 [Citations: 0]
  13. A three-dimensional explicit sphere function-based gas-kinetic flux solver for simulation of inviscid compressible flows

    Yang, L.M. | Shu, C. | Wu, J.

    Journal of Computational Physics, Vol. 295 (2015), Iss. P.322

    https://doi.org/10.1016/j.jcp.2015.03.058 [Citations: 37]
  14. A simplified discrete unified gas–kinetic scheme for compressible flow

    Zhong, Mingliang | Zou, Sen | Pan, Dongxin | Zhuo, Congshan | Zhong, Chengwen

    Physics of Fluids, Vol. 33 (2021), Iss. 3

    https://doi.org/10.1063/5.0033911 [Citations: 28]
  15. A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

    Yang, L. M. | Shu, C. | Wu, J.

    Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 6 P.887

    https://doi.org/10.4208/aamm.2015.m1172 [Citations: 34]
  16. EVALUATION OF THE PERFORMANCE OF THE HYBRID LATTICE BOLTZMANN BASED NUMERICAL FLUX

    ZHENG, H. W. | SHU, C.

    International Journal of Modern Physics: Conference Series, Vol. 42 (2016), Iss. P.1660152

    https://doi.org/10.1142/S2010194516601526 [Citations: 0]
  17. A lattice Boltzmann model for simulation of compressible flows

    Li, Kai | Zhong, Chengwen

    International Journal for Numerical Methods in Fluids, Vol. 77 (2015), Iss. 6 P.334

    https://doi.org/10.1002/fld.3984 [Citations: 23]
  18. Meshfree method based on discrete gas-kinetic scheme to simulate incompressible/compressible flows

    Zhan, Ningyu | Chen, Rongqian | You, Yancheng

    Physics of Fluids, Vol. 33 (2021), Iss. 1

    https://doi.org/10.1063/5.0033770 [Citations: 10]
  19. Meshfree lattice Boltzmann flux solver for compressible inviscid flows

    Zhan, Ningyu | Chen, Rongqian | Liu, Jiaqi | Qiu, Ruofan | You, Yancheng

    International Journal for Numerical Methods in Fluids, Vol. 93 (2021), Iss. 5 P.1378

    https://doi.org/10.1002/fld.4933 [Citations: 5]
  20. A rotated lattice Boltzmann flux solver with improved stability for the simulation of compressible flows with intense shock waves at high Mach number

    Chen, Jiabao | Yang, Dangguo | Chen, Qing | Sun, Jianhong | Wang, Yan

    Computers & Mathematics with Applications, Vol. 132 (2023), Iss. P.18

    https://doi.org/10.1016/j.camwa.2022.12.003 [Citations: 11]
  21. Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Power-Law Nanofluids in Rectangular Enclosures

    Wang, Lei | Chai, Zhenhua | Shi, Baochang

    Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 5 P.1094

    https://doi.org/10.4208/aamm.OA-2016-0066 [Citations: 11]
  22. Extension of lattice Boltzmann flux solver for simulation of 3D viscous compressible flows

    Yang, L.M. | Shu, C. | Wu, J.

    Computers & Mathematics with Applications, Vol. 71 (2016), Iss. 10 P.2069

    https://doi.org/10.1016/j.camwa.2016.03.027 [Citations: 22]
  23. An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures

    Huang, Xiaoyingjie | Chen, Jiabao | Zhang, Jun | Wang, Long | Wang, Yan

    Symmetry, Vol. 15 (2023), Iss. 10 P.1909

    https://doi.org/10.3390/sym15101909 [Citations: 1]
  24. A numerical study for WENO scheme-based on different lattice Boltzmann flux solver for compressible flows

    Li, You | Niu, Xiao-Dong | Yuan, Hai-Zhuan | Li, Xiang

    Acta Mechanica Sinica, Vol. 34 (2018), Iss. 6 P.995

    https://doi.org/10.1007/s10409-018-0785-9 [Citations: 6]
  25. Three-dimensional discrete Boltzmann models for compressible flows in and out of equilibrium

    Gan, Yanbiao | Xu, Aiguo | Zhang, Guangcai | Lai, Huilin

    Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 232 (2018), Iss. 3 P.477

    https://doi.org/10.1177/0954406217742181 [Citations: 9]