The incompressible Navier-Stokes equations are among the most widely used models to describe the flow of a Newtonian fluid (i.e. a fluid whose viscosity is independent of the external forces applied to the fluid). These equations model the fluid's velocity field and pressure field. The first of the two equations is none other than Newton's law, while the second derives from the conservation of mass in the case of an incompressible fluid (the divergence of velocity vanishes). The numerical approximation of these equations is a real challenge because of their three-dimensional and unsteady nature, the vanishing divergence constraint and the non-linearity of the convection term. Various discretisation methods exist, but for most of them, the mass conservation equation is not satisfied exactly. An alternative is to introduce the vorticity of the fluid as an additional unknown, equal to the curl of the velocity. The Navier-Stokes equations are then rewritten with three equations. The post-doc involves studying this formulation from a theoretical and numerical point of view and proposing an efficient algorithm for solving it, in the TrioCFD code.