| Abstract: | In this paper we develop a Fourier pseudospectral method forsolving two-dimensional vorticity equations. We prove the generalizedstability of the schemes and give convergence estimations dependingon the smoothness of the solution of the vorticity equations. Spectral methods have been applied widely to the partial differentialequations of fluid dynamics 4–11]. Guo Ben-yu proposeda technique to estimate strictly the error of the spectral schemesfor the K.D.V.-Burgers equation, the two-dimensional vorticityequations, and the Navier-Stokes equations 5,6,8]. On the otherhand, the authors 7,10] developed a pseudospectral method byusing Riesz spherical means to get better results. In this paper,we generalize this method to two-dimensional vorticity equations.The generalized stability and the convergence are proved. Thenumerical results show the advantage of such a method. |
