EI、Scopus 收录
中文核心期刊
Quick Search Issue Search Advanced Search
Volume 55 Issue 10
Oct.  2023
Turn off MathJax
Article Contents
Abstract
References
Related Articles
An Bo, Meng Xinyu, Yang Shuangjun, Sang Weimin. Research on the lattice Boltzmann algorithm for grid refinement based on non-uniform rectangular grid. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(10): 2288-2296. DOI: 10.6052/0459-1879-23-062
Citation: An Bo, Meng Xinyu, Yang Shuangjun, Sang Weimin. Research on the lattice Boltzmann algorithm for grid refinement based on non-uniform rectangular grid. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(10): 2288-2296. DOI: 10.6052/0459-1879-23-062
shu

RESEARCH ON THE LATTICE BOLTZMANN ALGORITHM FOR GRID REFINEMENT BASED ON NON-UNIFORM RECTANGULAR GRID

  • *.

    School of Aeronautic, Northwestern Polytechnic University , Xi’an 710072, China)

  • †.

    Key Laboratory of Icing and Anti/De-icing, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China

  • **.

    National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Xi’an 710072, China)

  • Received Date: February 27, 2023
  • Accepted Date: July 18, 2023
  • Available Online: July 19, 2023
    Graphical Abstract
    • Abstract
  • The traditional lattice Boltzmann method (LBM), especially the classic single-relaxation model (SLBM) based on the uniform square grid, has poor robustness and numerical stability, which limits the development and applications of LBM. Grid refinement strategy can effectively alleviate this dilemma, however for the traditional LBM, the grid refinement will inevitably lead to a sudden drop in computational efficiency and a rise in equipment requirements. Therefore, in order to solve this problem, based on the non-uniform rectangular grid, combined with the idea of interpolation LBM, the 25-bit Lagrangian interpolation LBM is proposed on the premise of ensuring the local grid refinement for the surfaces and area with severe flow changes, and the computational accuracy as well. Taking the classic lid-driven cavity flow for instance, a comparative analysis including different grid resolutions and interpolation schemes is performed. The verification includes both the numerical simulations of steady states and unsteady periodic solutions. The results show that the Lagrangian interpolation scheme performs better than other interpolation schemes. In this paper, the local grid refinement is able to ensure the capture of the flow details adjacent to surfaces and in the area of intense flow changes. The numerical algorithm can provide reliable results for numerical simulations. Meanwhile, the total grid number is greatly reduced, as a result the computational efficiency is greatly improved; The numerical simulation method has good robustness and is suitable for numerical simulations for both steady states and unsteady solutions.
    • FullText(HTML)
    • References (39)
  • [1]
    Chen SY, Doolen G. Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 1998, 143(2): 426-448
    [2]
    Benzi R, Succi S, Vergassola M, The lattice Boltzmann equation: theory and applications. Physics Reports, 1992, 222(3): 145-197
    [3]
    何雅玲, 王勇, 李庆. 格子Boltzmann方法的理论及应用. 北京: 科学出版社, 2009: 145-197

    He Yaling, Wang Yong, Li Qing. Lattice Boltzmann Method: Theory and Applications. Beijing: Science Press, 2009: 145-197 (in Chinese)
    [4]
    Silva G, Semiao V. First- and second-order forcing expansions in a lattice Boltzmann method reproducing isothermal hydrodynamics in artificial compressibility form. Journal of Fluid Mechanics, 2012, 698: 282-303
    [5]
    Yang LM, Shu C, Wu J. Development and comparative studies of three non-free parameter lattice Boltzmann models for simulation of compressible flows. Advances in Applied Mathematics and Mechanics, 2012, 4(4): 454-472
    [6]
    Jin Y, Uth MF, Kuznetsov AV, et al. Numerical investigation of the possibility of macroscopic turbulence in porous media: a direct numerical simulation study. Journal of Fluid Mechanics, 2015, 766: 76-103
    [7]
    Li XM, Leung RCK, So RMC. One-step aeroacoustics simulation using lattice Boltzmann method. AIAA Journal, 2006, 44(1): 78-79
    [8]
    Zhang CY, Cheng P, Minkowycz WJ. Lattice Boltzmann simulation of forced condensation flow on a horizontal cold surface in the presence of a non-condensable gas. International Journal of Heat and Mass Transfer, 2017, 115: 500-512
    [9]
    Chen S, Liu ZH, He Z, et al. A new numerical approach for fire simulation. International Journal of Modern Physics C, 2007, 118(2): 187-202
    [10]
    Haddadi H, Morris JF. Microstructure and rheology of finite inertia neutrally buoyant suspensions. Journal of Fluid Mechanics, 2014, 749: 431-459
    [11]
    An B, Bergadà JM, Mellibovsky F, et al. New Applications of numerical simulation based on lattice Boltzmann method at high Reynolds numbers. Computers & Mathematics with Applications, 2020, 79(6): 1718-1741
    [12]
    安博, 桑为民. 基于不同网格结构的LBM研究. 力学学报, 2013, 45(5): 699-706 (An Bo, Sang Weimin. The numerical study of lattice Boltzmann method based on different grid structure. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5): 699-706 (in Chinese)

    An Bo, Sang Weimin. The numerical study of lattice Boltzmann method based on different grid structure. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5): 699-706(in Chinese))
    [13]
    Mei RW, Shyy W. On the finite difference-based lattice Boltzmann method in curvilinear coordinates. Journal of Computational Physics, 1998, 143(2): 426-448
    [14]
    Guo ZL, Zhao TS. Explicit finite-difference lattice Boltzmann method for curvilinear coordinates. Physical Review E, 2003, 67(6): 066709
    [15]
    He XY, Doolen G. Lattice Boltzmann method on curvilinear coordinates system: Flow around a circular cylinder. Journal of Computational Physics, 1997, 134(2): 306-315
    [16]
    Marvriplis DJ. Multigrid solution of the steady state lattice Boltzmann equation. Computers & Fluids, 2006, 35: 793-804
    [17]
    Patil DV, Premnath KN, Banerjee S. Multigrid lattice Boltzmann method for accelerated solution of elliptic equations. Journal of Computational Physics, 2014, 265: 172-194
    [18]
    王兴勇, 索丽生, 程永光等. 双重网格lattice Boltzmann方法. 海河大学学报, 2003, 31(1): 5-10 (Wang Xingyong, Suo Lisheng, Cheng Yongguang, et al. Lattice Boltzmann method with double meshes. Journal of Hohai University, 2003, 31(1): 5-10 (in Chinese)

    Wang Xingyong, Suo Lisheng, Cheng Yongguang, et al. . Lattice Boltzmann method with double meshes. Journal of Hohai University, 2003, 31(1): 5-10(in Chinese))
    [19]
    Zhang Y, Xie JH, Li XY, et al. A multi-block adaptive solving technique based on lattice Boltzmann method. Modern Physics Letters B, 2018, 32(12-13): 1840052
    [20]
    Lagrava D, Malaspinas O, Latt J, et al. Advances in multi-domain lattice Boltzmann grid refinement. Journal of Computational Physics, 2012, 231: 4808-4822
    [21]
    Lin CL, Lai TG. Lattice Boltzmann method on composite grids. Physical Review E, 2000, 62(2): 2219-2225
    [22]
    Eitel-Amor G, Meinke M, Schrö der W. A lattice-Boltzmann method with hierarchically refined meshes. Computers & Fluids, 2013, 75: 127-139
    [23]
    Lu ZY, Liao Y, Qian DY, et al. Large eddy simulations of a stirred tank using the lattice Boltzmann method on a nonuniform grid. Journal of Computational Physics, 2002, 181: 675-704
    [24]
    Liu B, Khalili A. Acceleration of steady-state lattice Boltzmann simulations for exterior flows. Computers & Fluids, 2013, 75: 127-139
    [25]
    Valero-Lara P, Jansson J. A non-uniform staggered Cartesian grid approach for lattice-Boltzmann method. Procedia Computer Science, 2015, 51: 296-305
    [26]
    Zhou JG. A lattice Boltzmann method for solute transport. International Journal for Numerical Methods in Fluids, 2009, 61: 848-863
    [27]
    Zhou JG. A rectangular lattice Boltzmann method for groundwater flows. Procedia Computer Science, 2007, 21(9): 531-542
    [28]
    Qian YH, d’Humieres D, Lallemand P. Lattice BGK models for Navier-Stokes equation. Europhysics Letters, 1992, 17(6): 478-484
    [29]
    An B, Bergadà JM, Mellibovsky F. The lid driven right-angled isosceles triangular cavity flow. Journal of Fluid Mechanics, 2019, 875: 476-519
    [30]
    An B, Mellibovsky F, Bergadà JM, et al. Towards a better understanding of wall-driven square cavity flows using lattice Boltzmann method. Applied Mathematical Modelling, 2020, 82: 469-486
    [31]
    安博, 孟欣雨, 桑为民. 镜像对称顶盖驱动方腔内流过渡流临界特性研究. 力学学报, 2022, 54(9): 2409-2418 (An Bo, Meng Xinyu, Sang Weimin. On the transitional characteristics of mirror symmetry lid-driven cavity flow. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2409-2418 (in Chinese)

    An Bo, Meng Xinyu, Sang Weimin. On the transitional characteristics of mirror symmetry lid-driven cavity flow. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2409-2418(in Chinese))
    [32]
    An B, Guo SP, Bergadà JM. Lid driven triangular and trapezoidal cavity flow:Vortical structures for steady solutions and Hopf bifurcations. Applied Sciences, 2023, 13(2): 888
    [33]
    Guo ZL, Zheng CG, Shi BC. An extrapolation method for method boundary conditions in lattice Boltzmann method. Physics of Fluids, 2002, 14(6): 2007-2010
    [34]
    Ghia U, Ghia KN, Shin CT. High-Resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 1982, 48(3): 387-411
    [35]
    Erturk E, Gökçöl C. Fourth-order compact formulation of Navier-Stokes equations and driven cavity flow at high Reynolds numbers. International Journal for Numerical Methods in Fluids, 2005, 50(4): 421-436
    [36]
    Hou S, Zhou Q, Chen S, et al. Simulation of cavity flow by the lattice Boltzmann method. Journal of Computational Physics, 1995, 118(2): 329-347
    [37]
    Vanka S. Block implicit multigrid solution of Navier-Stokes equations in primitive variables. Journal of Computational Physics, 1986, 65(1): 138-158 doi: 10.1016/0021-9991(86)90008-2
    [38]
    Das MK, Rajesh Kanna P. Application of an ADI scheme for steady and periodic solutions in a lid-driven cavity problem. Journal of Numerical Methods for Heat & Fluid Flow, 2007, 17(8): 799-822
    [39]
    Shi X, Huang XW, Zheng Y, et al. A hybrid algorithm of lattice Boltzmann method and finite difference-based lattice Boltzmann method for viscous flows. International Journal for Numerical Methods in Fluids, 2017, 85(11): 641-661
    • Related Articles

  • Related Articles

    [1]Zou Lin, Zuo Hongcheng, Liu Diwei, Wang Jiahui, Xu Jinli. ACTIVE FLOW CONTROL OF WAVY CYLINDER BASED ON STEADY BLOWING AND SUCTION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 2970-2983. DOI: 10.6052/0459-1879-22-212
    [2]Yang Pengyu, Zhang Xin, Lai Qingren, Che Binghui, Chen Lei. EXPERIMENTAL INVESTIGATION OF THE INFLUENCE OF SCALING EFFECTS OF WINGS ON THE FLOW SEPARATION CONTROL USING PLASMA ACTUATORS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(12): 3321-3330. DOI: 10.6052/0459-1879-21-379
    [3]Zhang Wenwen, Xu Rongwu, He Lin, Pan Longde, Zhao Jiaxi. EXPERIMENTAL INVESTIGATION INTO THE CONTROL OF FLOW-INDUCED OSCILLATIONS OF UNDERWATER APERTURE-CAVITIES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(10): 2762-2775. DOI: 10.6052/0459-1879-21-143
    [4]Luo Kai, Wang Qiu, Li Yixiang, Li Jinping, Zhao Wei. RESEARCH PROGRESS ON MAGNETOHYDRODYNAMIC FLOW CONTROL UNDER TEST CONDITIONS WITH HIGH TEMPERATURE REAL GAS EFFECT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1515-1531. DOI: 10.6052/0459-1879-21-067
    [5]Huang Guangjing, Dai Yuting, Yang Chao. PLASMA-BASED FLOW CONTROL ON PITCHING AIRFOIL AT LOW REYNOLDS NUMBER[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(1): 136-155. DOI: 10.6052/0459-1879-20-183
    [6]Zhang Weiguo, Shi Zheyu, Li Guoqiang, Yang Yongdong, Huang Minqi, Bai Yunmao. NUMERICAL STUDY ON DYNAMIC STALL FLOW CONTROL FOR WIND TURBINE AIRFOIL USING PLASMA ACTUATOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1678-1689. DOI: 10.6052/0459-1879-20-090
    [7]Wang Wei, Zhang Qingdian, Tang Tao, An Zhaoyang, Tong Tianhao, Wang Xiaofang. MECHANISM INVESTIGATION OF WATER INJECTION ON SUPPRESSING HYDROFOIL CLOUD CAVITATION FLOW[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 12-23. DOI: 10.6052/0459-1879-19-282
    [8]Yiwen Li, Yutian Wang, Lei Pang, Lianghua Xiao, Zhiwen Ding, Pengzhen Duan. RESEARCH PROGRESS OF PLASMA/MHD FLOW CONTROL IN INLET[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 311-321. DOI: 10.6052/0459-1879-18-290
    [9]Yan Hong, Lin Ke. CONTROL MECHANISM OF THERMAL ACTUATOR IN SUPERSONIC ROUND JET[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4): 557-570. DOI: 10.6052/0459-1879-14-379
    [10]Chen Yaohui, Li Baoming, Pan Xuchao, Liu Yixin. RESEARCH OF THE CONTROL EFFICIENCY OF LIFT INCREASE AND DRAG REDUCTION BASE ON FLOW AROUND HYDROFOIL CONTROLLED BY LORENTZ FORCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(3): 414-421. DOI: 10.6052/0459-1879-14-346

  • Cited by

    Periodical cited type(9)

    1. 解浩，孟国亮，林小军，李宝栋. 前缘狭缝对NACA0015水翼非定常空化的影响. 机床与液压. 2025(04): 166-170 .
    2. 赵伟国，亢艳东，李清华，薛子阳. 叶片吸力面不同结构对离心泵空化初生的影响. 振动与冲击. 2022(07): 23-30 .
    3. 李智健，王巍，唐滔，安昭阳，纪祥，刘明雨. 主动射流抑制云空化及流致噪声的研究. 中国造船. 2022(04): 124-132 .
    4. 孙龙泉，颜皓，马贵辉，赵纪鹏. 环形槽对通气空泡融合的促进作用分析. 力学学报. 2021(02): 386-394 . 本站查看
    5. 陈国孝，刘喆，邵传平. 旋转振荡板尾流的控制研究. 力学学报. 2021(07): 1856-1875 . 本站查看
    6. 王恋舟，吴铁成，郭春雨. 螺旋桨梢涡不稳定性机理与演化模型研究. 力学学报. 2021(08): 2267-2278 . 本站查看
    7. 张珍，叶舒然，岳杰顺，王一伟，黄晨光. 基于组合神经网络的雷诺平均湍流模型多次修正方法. 力学学报. 2021(06): 1532-1542 . 本站查看
    8. 谢庆墨，陈亮，张桂勇，孙铁志. 基于动力学模态分解法的绕水翼非定常空化流场演化分析. 力学学报. 2020(04): 1045-1054 . 本站查看
    9. 胡建军，朱晴，王美达，金瑶兰，王思民，孔祥东. 近距离下射流冲击平板PIV实验研究. 力学学报. 2020(05): 1350-1361 . 本站查看

    Other cited types(12)

Catalog

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (543) PDF downloads (99) Cited by(21)
    Related

    Download Center

    Author Center

    Copyright © Editorial Office of the Chinese Journal of Mechanics   京ICP备05039218号-1

    Address：15 Beishihuan Xi Lu, Haidian District, Beijing, China   China Pos：100190

    Tel：010-62536271

    Email：lxxb@cstam.org.cn

    微信公众号
    RSS

    Supported by: Beijing Renhe Information Technology Co., Ltd.  Baidu Analytics

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return