The second-order projection method for the backward-facing step flow
The author reports the results on the incompressible flow past a backward-facing step by performing numerical computations of the unsteady two-dimensional Navier-Stokes equations with the second-order projection method within the laminar, transitional, and turbulent flow regimes. Cases of expansion ratios of \(2:1\) and \(3:2\) with the Reynolds number (Re) ranging from 25 to 5000 (based on the step height) have been investigated. For each time step of the computation, the projection method starts with the calculation of the velocity field with the prevailing pressure field, and the pressure field is subsequently corrected so that the resulting velocity field satisfies the continuity principle everywhere. When the Reynolds number is low, so that the flow remains laminar, excellent results have been produced and reported. For larger Re, the flow becomes unstable, transitional, and eventually turbulent. The author claims that there were no two-dimensional experimental data available for comparison. Nevertheless, some characteristics of the flow observed in three- dimensional experiments are verified in his numerical results. The author also notes that the approaching channel length is also important for relatively high Reynolds numbers. The reviewer would like to add that direct numerical simulation of the turbulent flow past a backward-facing step (by performing three- dimensional unsteady computations of the laminar Navier-Stokes equations) has been performed, and excellent results have been reported in the literature for such a flow in the laboratory with \(\text{Re} \approx 10^5\). However, it needed 1000 hours of computing time on supercomputer Cray-YMP.
scientific article; zbMATH DE number 758606