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

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

作　　者：邱周华 曾忠[4] 刘浩 QIU Zhouhua;ZENG Zhong;LIU Hao(Chongqing Southwest Research Institute for Water Transport Engineering,Chongqing Jiaotong University,Chongqing 400016,P.R.China;Key Laboratory of Transport Industry of Inland Waterway Regulation Engineering,Chongqing Jiaotong University,Chongqing 400074,P.R.China;Chongqing Xike Waterway Engineering Consulting Center,Chongqing 400016,P.R.China;College of Aerospace Engineering,Chongqing University,Chongqing 400044,P.R.China)

机构地区：[1]重庆交通大学重庆西南水运工程科学研究所,重庆400016 [2]重庆交通大学内河航道整治技术交通行业重点实验室,重庆400074 [3]重庆西科水运工程咨询中心,重庆400016 [4]重庆大学航空航天学院,重庆400044

出　　处：《应用数学和力学》2021年第2期142-150,共9页Applied Mathematics and Mechanics

基　　金：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)。

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P N×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.APN×PN-2 spectral element method based on the Picard linearized iteration was presented for the solution of 2D steady incompressible Navier-Stokes equations.Through the Picard iteration,the Navier-Stokes equations were converted to a series of Stokes-type equations to be solved with the PN×PN-2 spectral element method on the non-staggered grid in each iteration step.In order to eliminate the pseudo pressure mode,the pressure discretization is 2 orders lower than the velocity discretization,and the application of non-staggered grids makes the discretization of the equation convenient and avoids the interpolation error.The Stokes flow,the Kovasznay flow and the lid-driven cavity flow were simulated with the present method.The numerical results show that,the error converges with the spectral accuracy.In addition,avoidance of the pressure oscillation phenomenon indicates the accuracy and reliability of the present method.

关 键 词：定常NAVIER-STOKES方程 Picard迭代 谱元法 伪压力模 

分 类 号：O357.1[理学—流体力学]