Numerical solution to initial value problems for the Navier–Stokes equations in closed regions based on splitting method

On the basis of splitting method with respect to physical processes, a numerical method is proposed for solving initial value problems for the Navier– Stokes equations written in the terms of “eddy – current” variables. For the solution to the implicit difference systems a modified method of “two-field” (separate) calculation of the stream function and vorticite is suggested. For the first time in solving the Poisson equation for stream function two boundary conditions are simultaneously used on the boundaries ($\psi=\partial\psi/\partial n=0)$. A stability analysis in the linear approach is made. Some test numerical examples are given.