Non-uniqueness of a stationary viscous flow in the square lid-driven cavity

The article considers the classical benchmark problem in computational hydromechanics regarding a viscous incompressible flow in a square lid-driven cavity. An effective algorithm for solving a Navier–Stokes system of equations is proposed, that allows to construct stationary solutions on very detailed grids (up to $10^7$ grid points) for large (up to $10^5$) Reynolds numbers. Non-uniqueness of the stationary solution at large Reynolds numbers is shown. Special attention is given to the analysis of the main branch and one of the additional branches of the solution, appearing at relatively small $(\approx14000)$ Reynolds numbers.