A difference scheme for calculating unsteady Navier-Stokes equations

A difference scheme approximating the initial problem is proposed for an unsteady system of Navier-Stokes equations in (u, v, p) variables in a bounded region. The scheme is stable in the sense that, when certain conditions are fulfilled, the solution to the grid problem is bounded over an infinite time interval at arbitrary Reynolds numbers. The scheme provides for conservation of the continuity equation with prescribed accuracy. An algorithm for solving the system of grid equations is presented.