Cabaret scheme in “velocity–vorticity” formulation for numerical modeling of ideal fluid motion in two-dimensional domain

A modification of Cabaret scheme which was adapted for the numerical solution of ideal fluid motion equations in the variables “vorticity–velocity” was proposed. Dissipative and dispersive properties of the numerical algorithm were explored on example of isolated vortex problem. Decaying of homogeneous isotropic turbulence was simulated on grids of varying density. Spectral density of kinetic energy of obtained vortex flows were found to be fitting the “-3” law, which coincides to Kraichnan-Batchelor theory. Structural functions of simulated flows were found to be matching to the specific dimension law.