We investigate in this paper the application of Schwarz-based algorithms to compressible flows. First we study the combination of these methods with defect-correction procedures. We then study the effect on the Schwarz-based methods of replacing the explicit treatment of the boundary conditions by an implicit one. In the last part of this paper we study the combination of these methods with Newton-Krylov matrix-free methods. Numerical experiments that show the performance of our approaches are then presented. Tidriri, M. D. Unspecified Center NAS1-19480...