Immersed Boundary Methods (IBM) are a practical class of methods thatenable fluid computations in complex geometry while keeping a structuredmesh. Most of the existing IBM have been developed in the framework ofincompressible solvers, despite their significant interest to perform simula-tions in more complex configurations requiring a compressible solver. In thelast years, pressure based solvers met a growing interest to perform numericalsimulations of compressible flows, due to their attractive features, as remov-ing the stability condition on the acoustic time step, and being asymptoticallypreserving of the incompressible regime when the Mach number tends to zero.As this class of compressible solvers share many common features with classi-cal projection methods for incompressible flows, our objective in this paper isto present an adaptation of an efficient and accurate IBM developed for an in-compressible solver by Ng et al in [1] to a pressure based compressible solverrecently published by Urbano et al in [2]. The proposed algorithm benefits ofthe attractive properties of the original IBM proposed in [1] while being ableto undertake simulations in much more complex configurations. In particular,we will present validations and illustrations of the proposed solver in variousconfigurations as free-convection flows, acoustic waves propagating in a vari-able section pipe or interacting with a solid obstacle, as well as the descriptionof a thermal plasma during an electric arc discharge in a gas