On étudie des phénomènes de séparation d'écoulement avec deux approches différentes. Dans la première partie, on considère des écoulements 2D, instationnaires, incompressibles et non visqueux. Un modèle analytique-numérique, basé sur la jonction d'une transformation conforme et d'une méthode aux tourbillons ponctuels, est construit pour définir l'écoulement potentiel dans un domaine doublement connecté où les corps sont caractérisés par une variation temporelle de leur circulation. En particulier, on s'intéresse à l'étude de l'écoulement autour d'un VAWT avec deux pales. Dans la seconde partie on considère des écoulements visqueux et compressibles. On construit un solveur qui résoud les équations de Navier-Stokes en y introduisant une technique de pénalisation: les corps sont modélisés comme des milieux poreux ayant une porosité très petite par rapport à la porosité du fluide extérieur. Cette technique permet d'utiliser des maillages cartésiens pour des géométries très complexes. / In the present work flow separation phenomena are investigated by means of two different approaches. In the first part, 2D unsteady incompressible inviscid flows are studied. An analytical-numerical model, based on the conjunction of a conformal mapping and a point vortex method, is built to define the potential flow field in a doubly connected domain where bodies are characterized by a variation in time of their circulation. In particular, the study of the unsteady flow past a 2-blade Darrieus VAWT is addressed. Until now the study of vortex motions has only been described in doubly-connected flow fields where the circulations have a constant null value. The flow field here analysed has a deep unsteadiness, which determines the circulations varying in time: so a technique is developed to uniquely define the circulations around the bodies. Three conditions result necessary to be imposed: in addition to the two Kutta conditions at the trailing edges, another one has to be imposed in order to respect the Kelvin theorem. With a classical configuration, this machine, experiencing angles of attack of opposite values, gives rise to complex vortex shedding phenomena that reduce its performances and stress its structure. In order to control the flow separation from the blades, an innovative solution is qualitatively investigated which consists of taking blade profiles provided with vortex trapping cavities. Interesting results are obtained, even if in the limit of inviscid flow. In the second part compressible viscous flows are taken into account. A fully Navier-Stokes equations solver is implemented introducing the penalization technique. The idea is to replace the bodies by the fluid, in a way that also into the bodies the penalized Navier-Stokes equations remain valid, respecting the boundary conditions on their contours. Starting from this purpose, the bodies are considered as porous media with a little porosity with respect to that of the external flow, which tends to infinity. This technique allows simple Cartesian meshes to be used, also for very complex geometries like those of industrial interest. The resulting code is tested on different flow fields, both steady and unsteady, both subsonic and supersonic, obtaining always a good agreement with other theoretical and numerical results described in literature.