Spectral method of decoupling the vorticity and stream function for the incompressible fluid flows

A spectral method is proposed for the vorticity-stream function equations of the incompressible fluid flows. It is effective to overcome the lack of vorticity boundary condition. This method decouples the vorticity and stream function. At each time step, first, the vorticity is explicitly solved and the stream function is evaluated by a Poisson-like equation; then the vorticity is determined by a Poisson-like equation again. The numerical experiments show that this method is of efficiency and high accuracy.