In the thesis, a Virtual element method (VEM) is applied to a fluid dynamics problem. VEM is a numerical method that can be applied with general polygonal meshes to solve partial differential equations (PDE) problems. VEM allows the use of “hanging nodes”, nodes that divide two aligned edges of a mesh element. In this way local refinement is possible and it is useful to adapt the mesh where the physical problem requires. The fluid dynamics problem considers an incompressible flow inside a channel containing an obstacle, representing a square cylinder placed at the centre of the longitudinal axis. A parabolic velocity profile is assigned at the inflow.