The possibilities of applying the pure Lagrangian vortex methods of computational fluid dynamics to viscous incompressible flow simulations are considered in relation to various problem formulations. The modification of vortex methods-the Viscous Vortex Domain method-is used which is implemented in the VM2D code developed by the authors. Problems of flow simulation around airfoils with different shapes at various Reynolds numbers are considered: the Blasius problem, the flow around circular cylinders at different Reynolds numbers, the flow around a wing airfoil at the Reynolds numbers 104 and 105, the flow around two closely spaced circular cylinders and the flow around rectangular airfoils with a different chord to the thickness ratio. In addition, the problem of the internal flow modeling in the channel with a backward-facing step is considered. To store the results of the calculations, the POD technique is used, which, in addition, allows one to investigate the structure of the flow and obtain some additional information about the properties of flow regimes.
Keywords: Blasius boundary layer; channel with backward facing step; impulsively started cylinder; open source code; proper orthogonal decomposition; viscous vortex domain method; vortex particle method.