Study of a splitting difference scheme for the equations of motion of a viscous gas (Q1358078)

The two-dimensional Navier-Stokes equations for barotropic gas are considered assuming the double-periodic problem. A fractional-step scheme based on the splitting according to physical processes is described. Six fractional steps are introduced taking into account the pressure gradient, and the advection and viscous terms for two spatial direction successively. Discretizations at each stage result in explicit two-parametric time stepping for the pressure gradients and advection steps, while an implicit scheme is used for the viscous process. Assuming the CFL-type condition and some limitations imposed on the schemes parameters, the convergence theorems are proved showing first- and second-order convergence in time and space respectively.