Welcome to Journal of Beijing Institute of Technology
Volume 28Issue 3
.
Turn off MathJax
Article Contents
Dongdong Wan, Guichao Wang, Songying Chen. Numerical Investigation of Lid-Driven Deep Cavity with Local Grid Refinement of MRT-LBM[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2019, 28(3): 536-548. doi: 10.15918/j.jbit1004-0579.18030
Citation: Dongdong Wan, Guichao Wang, Songying Chen. Numerical Investigation of Lid-Driven Deep Cavity with Local Grid Refinement of MRT-LBM[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2019, 28(3): 536-548.doi:10.15918/j.jbit1004-0579.18030

Numerical Investigation of Lid-Driven Deep Cavity with Local Grid Refinement of MRT-LBM

doi:10.15918/j.jbit1004-0579.18030
  • Received Date:2018-06-06
  • In the case of lid-driven deep cavity flow, the effects of different resolutions of local grid refinement have been studied in the frame of multiple relaxation times (MRT) lattice Boltzmann method (LBM). In all the cases, the aspect ratio and Reynolds number are set as 1.5 and 3.200, respectively. First, the applied method is validated by comparing it with two reported works, with which agreements are reached. Then, six separate degrees of local grid refinement at the upper left corner, i.e. purely coarse grid, including 1/64, 1/32, 1/16, 1/8, 1/4 refinements of the lattice number in the width direction have been studied in detail. The results give the following indications:① The refinement degrees lower than 1/8 produce similar results; ② For single corner refinement, 1/4 refinement is adequate for clearing the noises in the singularity zone to a large extent;③ New noise around the interface between coarse and fine zones are introduced by local grid refinement. Finally, refinement of entire subzone neighboring the lid is examined to avoid introducing new noises and it has been found effective.
  • loading
  • [1]
    Chen S, Doolen G. Lattice Boltzmann method for fluid flows[J]. Annu Rev Fluid Mech, 1998, 30(1):329-364.
    [2]
    Yu D, Mei R, Luo L-S, et al. Viscous flow computations with the method of lattice Boltzmann equation[J]. Progr Aerospace Sci, 2003, 39(5):329-367.
    [3]
    Succi S. The lattice Boltzmann equation for fluid dynamics and beyond[M]. Oxford:Clarendon Press, 2001.
    [4]
    Chew Y, Shu C, Niu X. A new differential lattice Boltzmann equation and its application to simulate incompressible flows on non-uniform grids[J]. J Stat Phys, 2002, 107(1-2):329-342.
    [5]
    Bhatnagar P L, Gross E P, Krook M. A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component system[J]. Phys Rev, 1954, 94(3):511-525.
    [6]
    Lallemand P, Luo L-S. Theory of the lattice Boltzmann method:Dispersion, dissipation, isotropy, Galilean invariance, and stability[J]. Phys Rev E, 2000, 61(6):6546-6562.
    [7]
    Humieres D, Ginzburg I, Krafczyk M, et al. Multiple relaxation-time lattice Boltzmann models in three dimensions[J]. Philos Trans R Soc London A, 2002, 360(1792):437-451.
    [8]
    Mei R, Luo L-S, Lallemand P, et al. Consistent initial conditions for lattice Boltzmann simulation[J]. Comput Fluids,2006, 35(8):855-862.
    [9]
    Jahanshaloo L, Sidik N. Numerical simulation of high reynolds number flow structure in a lid-driven cavity using MRT-LES[J]. Applied Mechanics & Materials, 2014, 554:665-669.
    [10]
    Wang Y, Shu C, Yang L, et al. A decoupling multiple-relaxation-time lattice Boltzmann flux solver for non-Newtonian power-law fluid flows[J]. Journal of Non-Newtonian Fluid Mechanics, 2016, 235:20-28.
    [11]
    Ghia U, Ghia K N, Shin C T. High resolution for incompressible flow using the Navier-Stokes equations and a multi-grid method[J]. J Comput Phys, 1982, 48(3):387-411.
    [12]
    Chen S, Peng C, Teng Y, et al. Improving lattice Boltzmann simulation of moving particles in a viscous flow using local grid refinement[J]. Computers and Fluids, 2016, 136:228-246.
    [13]
    Filippova O, Hanel D. Grid refinement for latticeBGK models[J]. J Comput Phys, 1998, 147(1):219-228.
    [14]
    Filippova O, Hanel D. Acceleration of lattice-BGK schemes with grid refinement[J]. J Comput Phys, 2000, 165(2):407-427.
    [15]
    Crouse B, Rank E, Krafczyk M, et al. A LB-based approach for adaptive flow simulations[J]. Int J Mod Phys B, 2003, 17(01n02):109-112.
    [16]
    Yu D, Mei R, Shyy W. A multi-block lattice Boltzmann method for viscous fluid flows[J]. Int J Numer Methods Fluids, 2010, 39(2):99-120.
    [17]
    Yu D, Girimaji S. Multi-block lattice Boltzmann method:Extension to 3d and validation in turbulence[J]. Physica A, 2006, 362(1):118-24.
    [18]
    Farhat H, Lee J. Fundamentals of migrating multiblock lattice Boltzmann model for immiscible mixtures in 2D geometries[J]. Int J Multiphase Flow, 2010, 36(10):769-779.
    [19]
    Lagrava D, Malaspinas O, Latt J, et al. Advances in multi-domain lattice Boltzmann grid refinement[J]. J ComputPhys,2012, 231(14):4808-4882
    [20]
    Eitel-Amor G, Meinke M, Schroder W. A latticeBoltzmann method with hierarchically refined meshes[J]. Comput Fluids, 2013, 75(6):127-139.
    [21]
    Peng Y, Shu C, Chew Y, et al. Application of multi-block approach in the immersed boundary lattice Boltzmann method for viscous fluid flows[J]. J Comput Phys, 2006, 218(2):460-478.
    [22]
    Geller S, Tölke J, Krafczyk M. Lattice Boltzmann method on qudatree type gridsfor fluid structure interaction[M]//Fluid-Structure Interaction:Modelling, Simulation, Optimization. Berlin:Springer, 2006, 53:270-293.
    [23]
    Geller S, Krafczyk M, Tölke J, et al. Benchmark computations based on lattice Boltzmann, finite element and finite volume methods for laminar flows[J]. Comput Fluids, 2006b, 35(8):888-897.
    [24]
    Tölke J, Freudiger S, Krafczyk M. An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations[J]. Comput Fluids, 2006, 35(8):820-830.
    [25]
    Stiebler M, Krafczyk M, Freudiger S, et al. Lattice Boltzmann large eddy simulation of subcritical flows around a sphere on non-uniform grids[J]. Comput Math Appl, 2011, 61(12):3475-3484.
    [26]
    Geller S, Uphoff S, Krafczyk M. Turbulent jet computations based on MRT and cascaded lattice Boltzmann models[J]. Comput Math Appl, 2013, 65(12):1956-1966.
    [27]
    Fakhari A, Lee T. Numerics of the lattice Boltzmann method on non-uniform grids:standard LBM and finite-difference LBM[J]. Comput Fluids, 2015, 107(107):205-213.
    [28]
    Arora N, Gupta A, Shyy W. A shifting discontinuous-grid-block lattice Boltzmann method for moving boundary simulations[J]. Comput Fluids, 2016, 125:59-70.
    [29]
    Ghia U, Ghia K, Shin C. High-resolutions for incompressible flow using Navier-Stokes equations and a multigrid method[J]. J Comput Phys, 1982, 48(3):387-411.
    [30]
    Hou S, Zou Q, Chen S, et al. Simulation of cavity flow by the lattice Boltzmann method[J]. J Comput Phys, 1995, 118(2):329-347.
    [31]
    Guo Z, Shi B, Wang N. Lattice BGK model for incompressible Navier-Stokes equation[J]. J Comput Phys, 2000, 165(1):288-306.
    [32]
    Chew Y, Shu C, Niu X. A new differential lattice Boltzmann equation and its application to simulate incompressible flows on non-uniform grids[J]. J Stat Phys, 2002, 107(1-2):329-342.
    [33]
    Pan F, Acrivos A. Steady flows in rectangular cavities[J]. J Fluid Mech, 2006, 28(4):643-655.
    [34]
    Taneda S. Visualization of separating Stokes flows[J]. J Phys Soc Jpn, 1979, 46(6):1935-1941
    [35]
    Shen C, Floryan J. Low Reynolds number flow over cavities[J]. Phys Fluids, 1985, 28(11):3191-3202.
    [36]
    Gustafson K, Halasi A. Vortex dynamics of cavity flows[J]. J Comput Phys, 1986, 64(2):279-319.
    [37]
    Shankar P. The eddy structure in Stokes flow in a cavity[J]. J Fluid Mech,1993, 250:371-383.
    [38]
    Patil D, Lakshmisha K, Rogg B. Lattice Boltzmann simulation of lid-driven flow in deep cavities[J]. Computers & Fluids, 2004, 35(10):1116-1125.
    [39]
    Lin L, Chen Y, Lin C. Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity flows at different aspect ratios[J]. Computers & Fluids, 2011, 45(1):233-240.
    [40]
    Pedraza S, Toro J. Transient analysis of square and deep driven cavity for different re numbers by Lattice Boltzmann method (LBM)[J]. Mecanica Computational, 2010, 29:3763-3771.
    [41]
    Zhuo C, Zhong C, Cao J. Filter-matrix lattice Boltzmann simulation of lid-driven deep-cavity flows, Part I-Steady flows[J]. Computers & Mathematics with Applications, 2013, 65(12):1863-1882.
    [42]
    Zhuo C, Zhong C, Cao J. Filter-matrix lattice Boltzmann simulation of lid-driven deep-cavity flows, Part Ⅱ-Flow bifurcation[J]. Computers & Mathematics with Applications, 2013, 65(12):1883-1893.
    [43]
    Chen Songying, Wang Chao, Qu Yanpeng, et al. Local grid refinement implementation of lid driven cavity flow based on MRT-LBM[J]. Journal of Northeastern University, 2018, 39(4):538-542. (in Chinese)
  • 加载中

Catalog

    通讯作者:陈斌, bchen63@163.com
    • 1.

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (488) PDF downloads(371) Cited by()
    Proportional views
    Related

    /

      Return
      Return
        Baidu
        map