EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

佟莹 夏健 陈龙 薛浩天

佟莹, 夏健, 陈龙, 薛浩天. 基于隐式扩散的直接力格式浸没边界格子Boltzmann方法. 力学学报, 2022, 54(1): 94-105 doi: 10.6052/0459-1879-21-315
引用本文: 佟莹, 夏健, 陈龙, 薛浩天. 基于隐式扩散的直接力格式浸没边界格子Boltzmann方法. 力学学报, 2022, 54(1): 94-105 doi: 10.6052/0459-1879-21-315
Tong Ying, Xia Jian, Chen Long, Xue Haotian. An Immersed boundary lattice Boltzmann method based on implicit diffuse direct-forcing scheme. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 94-105 doi: 10.6052/0459-1879-21-315
Citation: Tong Ying, Xia Jian, Chen Long, Xue Haotian. An Immersed boundary lattice Boltzmann method based on implicit diffuse direct-forcing scheme. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 94-105 doi: 10.6052/0459-1879-21-315

基于隐式扩散的直接力格式浸没边界格子Boltzmann方法

doi: 10.6052/0459-1879-21-315
基金项目: 江苏高校优势学科建设工程资助项目
详细信息
    作者简介:

    陈龙, 讲师, 主要研究方向: 流固耦合动力学数值计算方法 . E-mail: lchen@nuaa.edu.cn

  • 中图分类号: O355

AN IMMERSED BOUNDARY LATTICE BOLTZMANN METHOD BASED ON IMPLICIT DIFFUSE DIRECT-FORCING SCHEME

  • 摘要: 采用浸没边界格子Boltzmann (immersed boundary-lattice Boltzmann, IB-LB)模型执行动边界绕流数值模拟时, 信息交互界面和边界力计算格式直接影响流动求解器的数值精度和计算效率. 基于隐式扩散界面, 一种改进的直接力格式IB-LB模型被提出. 边界力表达式基于欧拉/拉格朗日变量同一性准则推导, 转换矩阵描述的信息交互界面耦合了拉格朗日节点间的非同步运动. 采用Richardson迭代数值求解关联边界力与无滑移速度约束的线性方程组, 不仅克服了传统速度修正格式中矩阵求逆引起的计算效率问题, 而且摆脱了算法稳定性对拉格朗日点分布的依赖. 根据解析解已知的Taylor-Green涡流评估本文模型的数值模拟精度, 结果表明改进的IB模型能够完整保留背景LB模型的二阶数值精度. 静止圆柱和振荡圆柱绕流数值实验结果表明, 当前模型在涉及复杂外形和运动界面的流动模拟中能够提供可靠的数值预测, 满足力同一性的IB-LB模型能够有效抑制非定常流体力的伪物理震荡. 波动翼型绕流模拟验证了当前模型的实用性, 可在大变形柔性体流固耦合动力学问题中进一步推广.

     

  • 图  1  浸没边界方法原理图. ○ 代表拉格朗日边界节点; ●代表欧拉流体节点

    Figure  1.  Schematic diagram of the immersed boundary method. ○ indicate the Lagrangian boundary point; ● indicate the Eulerian fluid node

    图  2  直接力格式IB-LB模型算法流程图. 浅灰色框指明物面参数输出子步骤

    Figure  2.  An overview of one cycle of the IB-LB algorithm with the direct force scheme. The light grey box shows the output sub-step of the surface variables

    图  3  对数坐标下的速度误差L2与网格尺度h

    Figure  3.  Numerical error L2 of velocity versus mesh spacing h for Taylor-Green flow using the present IB-LB model with different φ and the standard LB model

    图  4  圆柱表面压强系数与方向角关系曲线

    Figure  4.  Pressure coefficient curve of cylinder versus the orientation angle

    图  5  圆柱周围流线分布

    Figure  5.  Streamline distribution near the cylinder.

    图  6  振荡圆柱阻力系数与圆柱中心位移的关系

    Figure  6.  Drag coefficient acting on the oscillation cylinder versus the position of the cylinder center

    图  7  波动翼型的时间相关推力系数

    Figure  7.  Time-dependent thrust coefficient acting on the undulatory foil

    图  8  波动翼型的时间相关运动功率系数、阻力功率系数和总功率系数

    Figure  8.  Time-dependent kinematic power coefficient, overcome drag power coefficient, and total power coefficient required by the undulatory foil

    图  9  均匀流动中复合运动翼型周围涡量云图

    Figure  9.  Vortex contour near the swimming foil in a uniform flow

    表  1  Re = 20和40时规则区长度和阻力系数与已有文献结果的比较

    Table  1.   Comparison of the obtained recirculating length, the drag coefficient with the previous results at Re = 20 and 40

    ReRefs.2Lw/DCD
    20Ref. [21]1.872.022
    Ref. [15]1.862.091
    Ref. [17]1.922.084
    Ref. [19]2.032.213
    present (30D×15D)1.902.266
    present (40D×40D)1.922.096
    40Ref. [21]4.671.495
    Ref. [15]4.621.565
    Ref. [17]4.721.560
    Ref. [19]4.821.660
    present (30D×15D)4.571.680
    present (40D×40D)4.601.572
    下载: 导出CSV

    表  2  Re = 100的当前模型与其他方法的流动特征参数比较

    Table  2.   Comparison between the present model and other methods at Re = 100

    Refs.$\overline{ {C}_{ {\rm{D} } } }$$ {C}_{{\rm{L}}}^{{\rm{max}}} $St
    Ref. [30]1.4200.3650.165
    Ref. [31]1.250.167
    Ref. [15]1.3640.3440.163
    Ref. [17]1.3680.3460.162
    Ref. [19]1.4180.3670.166
    present1.4450.3590.163
    下载: 导出CSV
  • [1] Peskin CS. The immersed boundary method. Acta Numerica, 2002, 11: 1-36
    [2] Mittal R, Iaccarino G. Immersed boundary methods. Annual Review of Fluid Mechanics, 2005, 37(1): 239-261
    [3] Huang WX , Tian FB. Recent trends and progress in the immersed boundary method. Journal of Mechanical Engineering Science, 2019, 233(23-24): 095440621984260
    [4] 杨明, 刘巨保, 岳欠杯等. 涡激诱导并列双圆柱碰撞数值模拟研究. 力学学报, 2019, 51(6): 1785-1796 (Yang Ming, Liu Jubao, Yue Qianbei, et al. Numerical simulation on the vortex-induced collision of two side-by-side cylinders. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1785-1796 (in Chinese) doi: 10.6052/0459-1879-19-224
    [5] Chen Shi yi, Doolen, et al. Lattice boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 1998, 30(1): 329-364
    [6] Rosis AD, Coreixas C. Multiphysics flow simulations using D3Q19 lattice Boltzmann methods based on central moments. Physics of Fluids, 2020, 32(11): 117101 doi: 10.1063/5.0026316
    [7] Karki P , Perumal DA , Yadav AK . Comparative studies on air, water and nanofluids based Rayleigh–Benard natural convection using lattice Boltzmann method: CFD and exergy analysis. Journal of Thermal Analysis and Calorimetry, 2021, 4: 231827396
    [8] 高铨, 邱翔, 夏玉显等. 基于LBM的壁湍流跨尺度能量传递结构统计. 力学学报, 2021, 53(5): 1257-1267 (Gao Quan, Qiu Xiang, Xia Yuxian, et al. Structure statistics of scale to scale energy transfer of wall turbulence based on LBM. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1257-1267 (in Chinese) doi: 10.6052/0459-1879-20-432
    [9] 白冰, 张涛, 李汉卿等. 基于不可压LBM的汽液两相流数值研究. 工程热物理学报, 2020, 41(8): 1952-1959 (Bai Bing, Zhang Tao, Li Hanqing, et al. A simulated study on liquid-gas flow based on incompressible LBM model. Journal of Engineering Thermophysics, 2020, 41(8): 1952-1959 (in Chinese)
    [10] 任彦霖, 刘赵淼, 逄燕等. 基于LBM的铝微滴斜柱沉积水平偏移研究. 力学学报, 2021, 53(6): 1599-1608 (Ren Yanlin, Liu Zhaomain, Pang Yang, et al. A lattice-Boltzmann method simulation of the horizontal offset in oblique column deposition of aluminum. Journal of Engineering Thermophysics, 2021, 53(6): 1599-1608 (in Chinese) doi: 10.6052/0459-1879-21-022
    [11] Feng, ZG, Michaelides EE. The immersed boundary-lattice Boltzmann method for solving fluid–particles interaction problems. Journal of Computational Physics, 2004, 195(2): 602-628
    [12] Feng ZG, Michaelides EE. Proteus: a direct forcing method in the simulations of particulate flows. Journal of Computational Physics, 2005, 202(1): 20-51
    [13] Niu XD, Shu C, Chew YT, et al. A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows. Physics Letters A, 2006, 354(3): 173-182 doi: 10.1016/j.physleta.2006.01.060
    [14] Shu C, Liu N, Chew YT. A novel immersed boundary velocity correction–lattice Boltzmann method and its application to simulate flow past a circular cylinder. Journal of Computational Physics, 2007, 226(2): 1607-1622
    [15] Wu J, Shu C. Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications. Journal of Computational Physics, 2009, 228(6): 1963-1979
    [16] Luo K, Wang Z, Fan J, et al. Full-scale solutions to particle-laden flows: Multidirect forcing and immersed boundary method. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2007, 76(6): 066709
    [17] Kang SK, Hassan YA. A comparative study of direct-forcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries. International Journal for Numerical Methods in Fluids, 2011, 66(9): 1132-1158
    [18] Dash SM, Lee TS, Lim TT, et al. A flexible forcing three dimension IB–LBM scheme for flow past stationary and moving spheres. Computers & Fluids, 2014, 95: 159-170
    [19] Yang H, Yuan H, Shi S, et al. An improved momentum exchanged-based immersed boundary–lattice Boltzmann method by using an iterative technique. Computers & Mathematics with Applications, 2014, 68(3): 140-155
    [20] 李桥忠, 陈木凤, 李游等. 浸没边界–简化热格子Boltzmann方法研究及其应用. 力学学报, 2019, 51(2): 392-404 (Li Qiaozhong, Chen Mufeng, Li You, et al. Numerical Study of the effect of forced pitching oscillation on rolling characteristics of vehicle. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 392-404 (in Chinese)
    [21] Wang Z, Wei Y, Qian Y. A bounce back-immersed boundary-lattice Boltzmann model for curved boundary. Applied Mathematical Modelling, 2020, 81: 428-440
    [22] Tao S , He Q , Chen B , et al. Distribution function correction-based immersed boundary lattice Boltzmann method for thermal particle flows. Computational Particle Mechanics, 2021, 8: 459-469
    [23] Huang R, Wu H. Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow. Journal of Computational Physics, 2016, 327: 121-139 doi: 10.1016/j.jcp.2016.09.030
    [24] Uhlmann, M. An immersed boundary method with the direct forcing for the simulation of particulate flow. Journal of Computational Physics, 2005, 209(2): 448-476
    [25] Qian YH, D'Humieres D, Lallemand P. Lattice BGK models for Navier-Stokes equation. EPL (Europhysics Letters), 1992, 17(6): 479
    [26] Guo Z, Zheng C, Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E, 2002, 65(4): 046308 doi: 10.1103/PhysRevE.65.046308
    [27] Sterling JD , Chen S. Stability analysis of lattice boltzmann methods. Journal of Compntational Physics, 1996, 123(1): 196-206
    [28] Yang X, Zhang X, Li ZL. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. Journal of Computational Physics, 2009, 228(20): 7821-7836
    [29] He X, Doolen G. Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder. Journal of Computational Physics, 1997, 134(2): 306-315 doi: 10.1006/jcph.1997.5709
    [30] Qin J, Yiannis A, Jiang X, et al. Efficient coupling of direct forcing immersed boundary lattice Boltzmann method and finite element method to simulate fluid structure interactions. International Journal for Numerical Methods in Fluids, 2020, 92(6): 545-572
    [31] Tritton DJ. Experiments on the flow past a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics, 1959, 6(4): 547-567
    [32] Shao X, Pan D, Jian D, et al. Hydrodynamic performance of a fishlike undulating foil in the wake of a cylinder. Physics of Fluids, 2010, 22(11): 918-328
    [33] Pan Y, Dong H. Computational analysis of hydrodynamic interactions in a high-density fish school. Physics of Fluids, 2020, 32(12): 121901 doi: 10.1063/5.0028682
  • 加载中
图(9) / 表(2)
计量
  • 文章访问数:  236
  • HTML全文浏览量:  62
  • PDF下载量:  54
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-06-30
  • 录用日期:  2021-09-27
  • 网络出版日期:  2021-09-28
  • 刊出日期:  2022-01-05

目录

    /

    返回文章
    返回