Numerical solutions of 2D steady incompressible backward-facing step flow at high Reynolds numbers

Numerical solutions of the test problem of 2D steady incompressible viscous flow over backward-facing step are presented in the article. The Navier-Stokes equations in a velocity-pressure formulation are numerically solved using a uniform grid of 6001´301 points. The control-volume technique for second-order difference approximation for spatial derivatives is used. The obtained numerical solutions were validated for a wide range of Reynolds numbers (100 £ Re £ 3000), comparing them to numerous experimental and numerical results found in the literature. The use of an original technology for building a solution at the exit from the channel (an open boundary of the solution domain) has made it possible to drastically reduce the length of the channel and, as a consequence, to decrease a size of the grid step. As a result, the increase in the stability of the computational algorithm took place, and it was possible to obtain solutions of the problem for large Reynolds numbers. Main research calculations have been performed for a short channel at Reynolds numbers from 1000 to 10000 with increment 1000. The obtained results have revealed a non-standard structure of primary vortex behind the step - numerous centers of rotation are present both in the vortex and under it in the area adjacent to the wall. It is shown that the number of the centers of rotation of the primary recirculation zone grows in accordance with the increase of the Reynoldsnumber. Also, the behavior of profiles of friction coefficients and hydrodynamic resistance to the flow depending on the Reynolds number are analyzed in the work. The obtained results may be useful for comparison and verification of solutions of this type of problems.