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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.
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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

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