Numerical simulation of viscous incompressible fluid in a short plane channel with backward-facing step

The paper presents the results of numerical simulation of viscous incompressible fluid in a plane channel in an area of its sudden expansion. The calculations are based on a solving of system of two-dimensional Navier–Stokes equations in ‘velocity-pressure’ variables in the range of Reynolds numbers $100\leqslant\mathrm{Re}\leqslant 3000$. Particular attention is paid to the behavior of the solution near exit boundary through which, in general, takes place as the inflow and outflow of liquid from the domain. The algorithm for solving of the Neumann problem for pressure modification is described in detail, in which as a correction technique the difference analogue of the necessary condition of existence of solution is used. It is shown that the received fields of speed and pressure have minimum deviations in a narrow zone near the exit boundary even in case of short channels, which lengths aren't enough for display a full vortex behind the backward facing step.