极坐标系下黏性流动的拟谱方法

Pseudo-spectral method in polar coordinate system for viscous flow

针对拟谱方法在极坐标下遇到的坐标奇异以及压力边界条件难处理等问题,提出了一种新的基于极坐标系下的拟谱方法.该方法在一致网格上直接求解非定常原始变量形式的N-S方程,采用算子分裂法来解耦速度和压力,在径向采用Chebyshev-Radau配置点,在角方向采用标准的Fourier配置点.同时对压力的谱导数矩阵进行了变换,使边界上的压力点不出现在计算方程中.把该方法应用于圆截面的曲线管道的层流流动中,数值实验结果表明,该方法成功解决了极坐标系中的坐标奇异问题;对压力谱导数矩阵的变换,避免了对压力提非物理的边界条件,保证了解的精度,同时也消除了虚假压力模式.

A new pseudo-spectral method based on polar coordinate system was presented to resolve the difficulty in the coordinate singularity and treatment of pressure boundary conditions. The method solves the unsteady Navier-Stokes equations in primitive variables form in regular grid system. The operator splitting scheme was adopted to decouple the pressure-velocity coupling. The Chebyshev-Radau nodes and standard Fourier nodes were chosen as collocation points in radial and azimuth direction. The spectral matrix of the pressure derivative was specially treated to exclude the boundary pressure points in the governing equations. The method＇s applications on the laminar flow in curved circular pipes show that the method has high accuracy and can eliminate the spurious modes of pressure.