Numerical simulation of viscous 2D lid-driven cavity flow at high Reynolds numbers

This paper addresses the question of existence of a steady-state solution to the problem of incompressible viscous fluid flow in a two-dimensional square cavity with a moving upper lid at high Reynolds numbers (Re>10000). Based on the literature survey and numerical results obtained when solving the problem at 10000≤Re≤20000, we have formulated the conditions for constructing the solution and discussed its distinguishing features. The calculated vortex parameters up to the fourth level are in good agreement with the results of other authors for Re=10000 and Re=20000, and this supports the validity of our results. For the same Reynolds numbers, the detailed structure of the flow is presented. The evolution of the fourth level bottom-corner vortices at 15000≤Re≤20000 is demonstrated. It is shown that at Re>10000 the fluid flow in the third and fourth level vortices has a clear Stokes mode. For these reasons, a comparison of the parameters of such vortices with the Moffatt analytical solution of fluid flow near sharp corners is performed. It has been found that the numerical and analytical results agree fairly well. Substantiation of the accuracy of the high-Re steady-state solution is carried out in the context of its saturation at an n-fold increase in the number of nodes along each spatial coordinate, false viscosity effect and solution convergence analysis of the behavior of dynamic systems.