格子玻尔兹曼法多块网格的交界结构优化研究
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摘要
基于格子玻尔兹曼方法LBM(Lattice Boltzmann Method)对多块网格方法(Multi-Block)的粗细网格交界结构进行了研究,提出了一种新的优化处理方案。解决了原有网格交界结构存在的三个问题,即两套插值运算造成的程序结构复杂的问题,存储前几个时间步的节点流场数据以备插值运算造成内存浪费的问题和基于时间插值结果进行空间插值计算造成插值误差积累的问题。用一次多点二维空间插值的方式,将原方法的空间和时间双插值,简并成一次空间插值。通过对经典的非定常的圆柱绕流算例和定常的标准顶盖方腔驱动流算例的仿真模拟,验证了交界面处质量、动量及应力的连续性以及网格交界面数据过渡的流畅度,最终验证了改进方法的正确性。数值模拟结果表明,改进后多块算法可实现局部网格细化,进一步推动LBM方法在实际工程问题中的应用。
An optimal plan of mesh interface between the coarse and fine mesh of Multi-Block method is proposed based on the Lattice Boltzmann Method in this paper.Three key problems in the original mesh interface are effectively solved,namely,the problem of complex programming due to two sets of interpolation operations,memory waste caused by the flow data of the several past time steps is stored for the time interpolation,and accumulative interpolation error due to spatial interpolated interpolation.A new kind of coarse mesh overlapping is developed,in which the interpolation of the original space and time is simplified into a spatial interpolation by means of two-dimensional multi-point spatial interpolation.Classic examples of unsteady flow around a circular cylinder and driven flow of square cavity are analysed.The continuity of mass,momentum and stress at the interface and smoothness of transition of the interface data are verified.The computational results show that the improved Multi-Block algorithm can realize the local mesh refinement,and further promote the application of LBM in practical engineering problems.
An optimal plan of mesh interface between the coarse and fine mesh of Multi-Block method is proposed based on the Lattice Boltzmann Method in this paper.Three key problems in the original mesh interface are effectively solved,namely,the problem of complex programming due to two sets of interpolation operations,memory waste caused by the flow data of the several past time steps is stored for the time interpolation,and accumulative interpolation error due to spatial interpolated interpolation.A new kind of coarse mesh overlapping is developed,in which the interpolation of the original space and time is simplified into a spatial interpolation by means of two-dimensional multi-point spatial interpolation.Classic examples of unsteady flow around a circular cylinder and driven flow of square cavity are analysed.The continuity of mass,momentum and stress at the interface and smoothness of transition of the interface data are verified.The computational results show that the improved Multi-Block algorithm can realize the local mesh refinement,and further promote the application of LBM in practical engineering problems.
引文
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[16] Yuan H Z,Niu X D,Shu S,et al.A momentum exchange -based immersed boundary-lattice Boltzmann method for simulating a flexible filament in an incompressible flow [J].Computers & Mathematics with Applications,2014,67(5):1039-1056.
[17] Liu C,Zheng X,Sung C H.Preconditioned multigrid methods for unsteady incompressible flows [J].Journal of Computational Physics,1998,139(1):35-57.
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[19] Rajani B N,Kandasamy A,Majumdar S.Numerical simulation of laminar flow past a circular cylinder[J].Applied Mathematical Modelling,2009,33(3):1228-1247.
[20] 刘祖斌,赵鹏.结合大涡模拟的格子玻尔兹曼方法模拟高雷诺数流动[J].船舶力学,2015,19(5):484-492.(LIU Zu-bin,ZHAO Peng.High-Re flow simulation with Lattice Boltzmann method combined with LES [J].Journal of Ship Mechanics,2015,19(5):484-492.(in Chinese))
[21] Ghia U,Ghia K N,Shin C T.High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method [J].Journal of Computational Physics,1982,48(3):387-411.
[2] Chen S,Doolen G D.Lattice Boltzmann method for fluid flows [J].Annual Review of Fluid Mechanics,1998,30(1):329-364.
[3] 史冬岩,王志凯,张阿漫.一种模拟气液两相流的格子玻尔兹曼改进模型[J].力学学报,2014,46(2):224-233.(SHI Dong-yan,WANG Zhi-kai,ZHANG A-man.A novel Lattice Boltzmann model simulating gas -liquid two -phase flow [J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):224-233.(in Chinese))
[4] 杨帆,施徐明,郭雪岩,等.多弛豫时间格子玻尔兹曼方法的分块算法[J].排灌机械工程学报,2013,31(1):56-60.(YANG Fan,SHI Xu-ming,GUO Xue -yan,et al.Multi-block scheme of MRT lattice Boltzmann method for viscous fluid flow[J].Journal of Drainage and Irrigation Machinery Enginee -ring,2013,31(1):56-60.(in Chinese))
[5] 王龙,宋文萍.翼型超低雷诺数气动特性研究[J].西北工业大学学报,2011,29(2):165-170.(WANG Long,SONG Wen-ping.Exploring with multi-block LBM aerodynamic characteristics of airfoil at ultra-low Reynolds number [J].Journal of Northwestern Polytechnical University,2011,29(2):165-170.(in Chinese))
[6] 何雅玲,王勇,李庆.格子Boltzmann方法的理论及应用[M].北京:科学出版社,2009.(HE Ya-ling,WANG Yong,LI Qing.Lattice Boltzmann Method:Theory and Applications[M].Beijing:Science Press,2009.(in Chinese))
[7] Filippova O,H?nel D.Grid refinement for Lattice-BGK models [J].Journal of Computational Phy-sics,1998,147(1):219-228.
[8] Yu D,Mei R,Shyy W.A multi-block lattice Boltzmann method for viscous fluid flows [J].International Journal for Numerical Methods in Fluids,2002,39(2):99-120.
[9] Farhat H,Lee J S.Fundamentals of migrating multi-block lattice Boltzmann model for immiscible mixtures in 2D geometries [J].International Journal of Multiphase Flow,2010,36(10):769-779.
[10] Liu H,Zhou J G,Burrows R.Multi-block lattice Boltzmann simulations of subcritical flow in open channel junctions [J].Computers & Fluids,2009,38(6):1108-1117.
[11] Bhatnagar P L,Gross E P,Krook M.A model for co -llision processes in gases.I:Small amplitude processes in charged and neutral one -component systems [J].Physical Review,1954,94(3):511-525.
[12] Sauer T,Xu Y.On multivariate Lagrange interpolation[J].Mathematics of Computation,1995,64(211):1147-1170.
[13] 郭照立,郑楚光.格子Boltzmann方法的原理及应用[M].北京:科学出版社,2009.(GUO Zhao-li,ZHENG Chu-guang.Theory and Applications of Lattice Boltzmann Method[M].Beijing:Science Press,2009.(in Chinese))
[14] 史冬岩,王志凯,张阿漫.任意复杂流-固边界的格子Boltzmann处理方法[J].物理学报,2014,63(7):213-221.(SHI Dong-yan,WANG Zhi-kai,ZHANG A-man.A novel lattice Boltzmann method for dealing with arbitrarily complex fluid-solid boundaries [J].Acta Physica Sinica,2014,63(7):213-221.(in Chinese))
[15] Wang X,Shu C,Wu J,et al.A boundary condition-implemented immersed boundary-lattice Boltzmann method and its application for simulation of flows around a circular cylinder [J].Advances in Applied Mathematics and Mechanics,2014,6(6):811-829.
[16] Yuan H Z,Niu X D,Shu S,et al.A momentum exchange -based immersed boundary-lattice Boltzmann method for simulating a flexible filament in an incompressible flow [J].Computers & Mathematics with Applications,2014,67(5):1039-1056.
[17] Liu C,Zheng X,Sung C H.Preconditioned multigrid methods for unsteady incompressible flows [J].Journal of Computational Physics,1998,139(1):35-57.
[18] Ye T,Mittal R,Udaykumar H S,et al.An accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries [J].Journal of Computational Physics,1999,156(2):209-240.
[19] Rajani B N,Kandasamy A,Majumdar S.Numerical simulation of laminar flow past a circular cylinder[J].Applied Mathematical Modelling,2009,33(3):1228-1247.
[20] 刘祖斌,赵鹏.结合大涡模拟的格子玻尔兹曼方法模拟高雷诺数流动[J].船舶力学,2015,19(5):484-492.(LIU Zu-bin,ZHAO Peng.High-Re flow simulation with Lattice Boltzmann method combined with LES [J].Journal of Ship Mechanics,2015,19(5):484-492.(in Chinese))
[21] Ghia U,Ghia K N,Shin C T.High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method [J].Journal of Computational Physics,1982,48(3):387-411.