The implicit line-by-line recurrence method in application to the solutionof problems of incompressible viscous fluid dynamics

In the paper the results of applying the implicit line-by-line recurrence method for solving of systems of elliptic difference equations, arising, in particular, at numerical simulation of dynamics ofincompressible viscous fluid are considered. Research is conducted on the example of the problem about asteady-state two-dimensional lid-driven cavity flow formulated in primitive variables ( u , v , p ) for large Re (up to20 000) and grids (up to 2049$\times$2049). High efficiency of the method at calculation of a pressure correction fieldsis demonstrated. The difficulties of constructing a solution of the problem for large Rе are analyzed.