Fast algorithms for calculations of viscous incompressible flows using the artificial compressibility method

The velocity correction method is designed to simulate stationary and non-stationary, two- and three-dimensional motions of a viscous incompressible fluid. The basic assumption of this method consists in splitting the velocity and the pressure fields and calculations are performed in two steps. In the first step, a tentative velocity field is determined by simplified equations for momentum conservation. In the second step the Neumann problem for the Poisson equations is solved to obtain the computational pressure, and the velocity components are corrected. A standard method of lines approach and the two grids method are applied in this contribution. Some test calculations for laminar and transitional flows in square and cubic cavities with one moving wall as well as in a backward-facing step are reported