谱方法求解非惯性系中二维不可压缩渠道流

用谱方法求解了非惯性系中二维不可压缩渠道流动.控制方程采用原始变量提法,外力包括非惯性动系的线加速度以及转动角速度和角加速度引起的惯性力和科氏力.压强用Poisson方程求解.流向用Fourier多项式离散,竖向用Chebyshev多项式离散.将边界条件用谱多项式展开,在谱空间用Chebyshev-tau方法时间推进求解半隐式离散的速度方程和直接求解压强方程.利用该算法,分别计算了动系作匀速转动和加速转动时的二维渠道流动.并将计算结果与控制体积分方程所作的理论分析作了比较,结果互相符合.

A Fourier-Chebyshev Spectral Method for Solving 2D Incompressible Channel Flow in Non-inertia Coordinate System

Time-dependent incompressible Navier-Stokes equations in primitive variable form with body forces of an apparent force are established,and a coriolis force caused by the linear acceleration,angular speed and angular acceleration of the generalized non-inertial coordinate system is expressed.The equations are numerically solved by a Fourier-Chebyshev spectral method,where Fourier polynomials are used in the streamwise discretization and Chebyshev modes in the transverse direction.With the boundary conditions expanded by spectral polynomials,the Chebyshev-tau methods are used to construct numerical integration of the momentum equations and pressure Poisson equations.The above spectral methods are applied in 2D channel flow with the kinetic reference system rotating at a constant and accelerating speed.The numerical results agree well with that from the theoretical analysis of the control integral equations.