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在数值模拟领域内,谱方法具有收敛快、分辨率高和精度高的优点.谱方法处理边界方便,随着数值方法的改善和计算机的发展,它在数值模拟中的作用愈加重要.这里采用谱方法数值求解三维N-S方程,用这一方法计算了直槽道内流体的流动.计算得到的层流和湍流结果与理论结果符合地较好.在此基础之上进一步模拟了几种不同槽道内的三维粘性流体层流流动,特别在弯曲槽道内的流动计算中,发展了源项处理方法,正确地反映了弯曲固壁对流体流动的影响.通过对湍流计算获得的脉动速度场的统计可以得到湍流运动的许多统计量,正确地反映了湍流运动的特征,说明可以用模拟得到的流场来代替真实的流场.进行了气固两相流动的研究,由直接模拟得到的流体瞬时速度场对固体粒子的作用进行了粒子运动的模拟计算,得到了颗粒在真实流场中运动的浓度,轨道等有用信息和运动特性,得到了令人鼓舞的结果.“,”In this paper we used a spectral method to solve the three--dimensional N--S equationsfor the flow in the various channels and investigate the particle motion in them. Fourier seriesis utilized on the x and z directions, which both parallel to the surface of channel, Chebyshevpolynomial is utilized on the y direction. Crank--Nicholson form and Adam--Bashforth formare adopted for the viscous term and the non--linear term respectively. The fluid flow weresimulated in several channels by spectral method. Numerical results and analytical resultsare agreed with each other fairly well, which prove that the spectral method is an efficientmethod to simulate N--S equations. And preliminary effort has been made to curve tunnel.