Сabaret scheme for the two-dimensional incompressible fluid in terms of «stream function – vorticity»

In present article Cabaret-method was generalized in case of two-dimensional incompressible fluid in terms of «stream function – vorticity». The example test «one-eddy» problem shows the high quality of the received scheme from the standpoint of the question of dispersion and diffusion properties. In the problem of decaying homogeneous isotropic turbulence slope of the energy spectra for all grids (16$\times$16, 32$\times$32, 64$\times$64, 128$\times$128) are «$-3$» up to the highest harmonics, which coincides with the theory of Batchelor.