Spectral Method for Vorticity-Stream Function Form of Navier-Stokes Equations in an Infinite Channel with Slip Boundary Conditions

In this paper, we propose a spectral method for the vorticity-stream function form of Navier-Stokes equations in an infinite channel with slip boundary conditions by using Laguerre functions. The numerical solutions fulfill the incompressibility and the physical boundary conditions automatically. The stability and the spectral accuracy in space of proposed method are proved. Numerical results demonstrate the high efficiency of suggested algorithm, and coincide the analysis very well.