Cabaret scheme for two-dimensional incompressible fluid in terms of the stream function-vorticity variables

Abstract

In the present work, the Cabaret method is generalized to the case of two-dimensional incompressible fluid in terms of the stream function-vorticity variables. Using the example of the solitary vortex problem, the high quality of the obtained algorithm in terms of its dissipative and dispersion properties is demonstrated. In the problem about decaying homogeneous isotropic turbulence, the slopes of the energy spectra for all grids (16 × 16, 32 × 32, 64 × 64, 128 × 128) are (−3) up to the highest harmonics, which coincides with Batchelor’s theory.