In order to exploit the capabilities of Computational Fluid Dynamics in aerodynamic design, the cost should be reduced without compromising accuracy and consistency. In this direction a hybrid methodology is formulated within the context of domain decomposition. The strategy is to choose in each sub-domain the best performing method. Close to solid boundaries a grid-based Eulerian flow solver is used while in the far field the flow is described in Lagrangian coordinates using particle approximations. Aiming at consistently including compressible effects, particles carry mass, dilatation, vorticity and energy and the complete set of conservation laws is solved in Lagrangian coordinates. At software level, the URANS solver MaPFlow is coupled to the vortex code GENUVP. In the present paper the two dimensional formulation is given alongside with validation tests around airfoils in steady and inherently unsteady conditions. It is verified that: purely Eulerian and hybrid simulations are equivalent; the Eulerian domain in the hybrid solver can be effectively restricted to a layer 1.5 chord lengths wide; significant cost reduction reaching up to 1:3 ratio is achieved.