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Numerical simulation of channel flow with the spectral method

机译：谱法数值模拟河道水流

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摘要

In the field of numericla smulation,spectral method has the merits of quick convergence,high rsolution,and high accuracy.Here we used a spectral mehtod to solve the three-dimensional N-S equations for the flow in the various channels.Fourier series is utilized on the x and z diretions,which both parallel to the surface of channel,Chebyshev polnomia is utilized on the y direction.Crank-Nicholsonfrom and Adam-Bashfroth form are adopted for the viscous term and the non-linear term resectively.the boundary condition and continuity equations are satisfied accurately in this solution.The fluid flow were simulated in several channels by spectral method.Numerical results and analytical results are agreed with each other fairly well,which prove that the spectral method is an efficent mehtod to simulate N-S equations.And preliminary effort has been made to curve tunnel.
机译：在数值模拟领域，频谱法具有收敛速度快，解像度高，精度高的优点。在此我们使用频谱法来求解各个通道中的三维NS方程。利用傅立叶级数x和z方向都与通道表面平行，在y方向上使用Chebyshev polnomia。粘性项和非线性项分别采用了来自Crank-Nicholson和Adam-Bashfroth的形式。边界条件和该解决方案能够准确地满足连续性方程。采用谱方法在多个通道中模拟了流体流动。数值结果和分析结果相互吻合得很好，证明了谱方法是模拟NS方程的有效方法。弯道的初步研究已经完成。

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