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Picard迭代的PN×PN-2谱元法求解定常不可压缩Navier-Stokes方程

邱周华 曾忠 刘浩

邱周华, 曾忠, 刘浩. 基于Picard迭代的PN×PN-2谱元法求解定常不可压缩Navier-Stokes方程[J]. 应用数学和力学, 2021, 42(2): 142-150. doi: 10.21656/1000-0887.410289
引用本文: 邱周华, 曾忠, 刘浩. 基于Picard迭代的PN×PN-2谱元法求解定常不可压缩Navier-Stokes方程[J]. 应用数学和力学, 2021, 42(2): 142-150. doi: 10.21656/1000-0887.410289
QIU Zhouhua, ZENG Zhong, LIU Hao. A PN×PN-2 Spectral Element Method Based on the Picard Iteration for Steady Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 142-150. doi: 10.21656/1000-0887.410289
Citation: QIU Zhouhua, ZENG Zhong, LIU Hao. A PN×PN-2 Spectral Element Method Based on the Picard Iteration for Steady Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2021, 42(2): 142-150. doi: 10.21656/1000-0887.410289

基于Picard迭代的PN×PN-2谱元法求解定常不可压缩Navier-Stokes方程

doi: 10.21656/1000-0887.410289
基金项目: 重庆市基础与前沿研究计划项目(cstc2015jcyjA00010);重庆市教委科学技术研究项目(KJ1600523)
详细信息
    作者简介:

    邱周华(1986—),男,助理研究员,博士(通讯作者. E-mail: zhqiu@cqjtu.edu.cn).

  • 中图分类号: O357.1

A PN×PN-2 Spectral Element Method Based on the Picard Iteration for Steady Incompressible Navier-Stokes Equations

  • 摘要: 该文给出了一种求解二维定常不可压缩Navier-Stokes方程的基于Picard线性化迭代的PN×PN-2谱元法.通过Picard线性化将不可压缩Navier-Stokes方程的求解转化为一系列线性的Stokes-type方程,再利用非交错网格的PN×PN-2谱元法计算每个迭代步的Stokes-type方程.为了消除伪压力模,压力离散比速度离散低两阶,非交错网格的应用使得方程的离散方便且不会带来相应的插值误差,从而保证了谱精度.通过此方法数值计算了有精确解的Stokes流动、Kovasznay流动和方腔顶盖驱动流,结果表明,迭代收敛非常快,误差收敛达到了谱精度收敛,并且避免了压力震荡的出现,表明了该文方法准确可靠.
  • [1] AUTERI F, GUERMOND J L, PAROLINI N. Role of the LBB condition in weak spectral projection methods[J]. Journal of Computational Physics,2001,174(1): 405-420.
    [2] SCHUMACK M R, SCHULTZ W W, BOYD J P. Spectral method solution of the Stokes equations on nonstaggered grids[J]. Journal of Computational Physics,1990,89(2): 30-58.
    [3] DEBLOIS B M. Linearizing convection terms in the Navier-Stokes equations[J]. Computer Methods in Applied Mechanics and Engineering,1997,143(3/4): 289-297.
    [4] REHMAN M U, VUIK C, SEGAL G. Numerical solution techniques for the steady incompressible Navier-Stokes problem[C]// Proceedings of the World Congress on Engineering.London, 2008: 844-849.
    [5] 苏铭德, 陈霜立. 定常不可压缩粘性流体流动Navier-Stokes方程的推进迭代法[J]. 计算物理, 1989,6: 321-334.(SU Mingde, CHEN Shuangli. Solution of the N-S equation of the steady incompressible viscous flow with marching-iterative method[J]. Chinese Journal of Computational Physics,1989,6: 321-334.(in Chinese))
    [6] CASARIN M A. Schwarz preconditioners for the spectral element discretization of the steady Stokes and Navier-Stokes equations[J]. Numerische Mathematik,2001,89: 307-339.
    [7] PONTAZA J P, REDDY J N. Spectral/hp least-squares nite element formulation for the Navier-Stokes equations[J]. Journal of Computational Physics,2003,190: 523-549.
    [8] KNOLL D A, KEYES D. Jacobian-free Newton-Krylov methods: a survey of approaches and applications[J]. Journal of Computational Physics,2004,193: 357-397.
    [9] 马东军, 柳阳, 孙德军, 等. 高阶谱元区域分解算法求解定常方腔驱动流[J]. 计算力学学报, 2006,23(6): 668-673.(MA Dongjun, LIU Yang, SUN Dejun, et al. Spectral element method with a domain decomposition Stokes solver for steady cavity driven flow[J]. Chinese Journal of Computational Mechanics,2006,23(6): 668-673.(in Chinese))
    [10] ZHANG W, ZHANG C H, XI G. An explicit Chebyshev pseudospectral multigrid method for incompressible Navier-Stokes equations[J]. Computers & Fluids,2010,39(1): 178-188.
    [11] 章争荣, 张湘伟. 二维定常不可压缩粘性流动N-S方程的数值流形方法[J]. 计算力学学报, 2010,27(3): 415-421.(ZHANG Zhengrong, ZHANG Xiangwei. Numerical manifold method for steady incompressible viscous 2D flow Navier-Stokes equtions[J]. Chinese Journal of Computational Mechanics,2010,27(3): 415-421.(in Chinese))
    [12] 覃燕梅, 冯民富, 罗鲲, 等. Navier-Stokes方程的局部投影稳定化方法[J]. 应用数学和力学, 2010,31(5): 618-630.(QIN Yanmei, FENG Minfu, LUO Kun, et al. Local projection stabilized finite element method for the Navier-Stokes equations[J]. Applied Mathematics and Mechanics,2010,31(5): 618-630.(in Chinese))
    [13] HE Y, ZHANG Y, SHANG Y, et al. Two-level Newton iterative method for the 2D/3D steady Navier-Stokes equations[J]. Numerical Methods for Partial Differential Equations,2012,28: 1620-1642.
    [14] MELCHIOR S A, LEGAT V, DOOREN P V, et al. Analysis of preconditioned iterative solvers for incompressible flow problems[J]. International Journal for Numerical Methods in Fluids,2012,68: 269-286.
    [15] OZCELIKKALE A, SERT C. Least-squares spectral element solution of incompressible Navier-Stokes equations with adaptive refinement[J].Journal of Computational Physics,2012,231: 3755-3769.
    [16] 戴海, 潘文峰. 谱元法求解Helmholtz方程透射特征值问题[J]. 应用数学和力学, 2018,39(7): 833-840.(DAI Hai, PAN Wenfeng. A spectral element method for transmission eigenvalue problems of the Helmholtz equation[J]. Applied Mathematics and Mechanics,2018,39(7): 833-840.(in Chinese))
    [17] 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.
    [18] AIDUN C K, TRIANTAFILLOPOULOS N G, BENSON J. Global stability of a lid-driven cavity with through-flow: flow visualization studies[J].Physics of Fluids A: Fluid Dynamics,1991,3(9): 2081-2091.
    [19] ALBENSOEDER S, KUHLMANN H C, RATH H J. Three-dimensional centrifugal-flow instabilities in the lid-driven-cavity problem[J]. Physics of Fluids,2001,13: 121-135.
    [20] THEOFILIS V. Global linear instability[J]. Annual Review of Fluid Mechanics,2011,43: 319-352.
    [21] KOSEFF J R, STREET R L. The lid-driven cavity flow: a synthesis of qualitative and quantitative observations[J]. Journal of Fluids Engineering,1984,106(4): 390-398.
    [22] KOSEFF J R, STREET R L, GRESHO P M, et al. A three-dimensional lid-driven cavity flow: experiment and simulation[C]// International Conference on Numerical Methods in Laminar and Turbulent Flow.Seattle, WA, 1983.
  • 加载中
计量
  • 文章访问数:  1115
  • HTML全文浏览量:  261
  • PDF下载量:  364
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-09-24
  • 修回日期:  2020-10-12
  • 刊出日期:  2021-02-01

目录

    /

    返回文章
    返回