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In this article the finite volume method (FVM) is carried out to simulate the flow around and through a two-dimensional porous cylinder. An external magnetic field is used to control the wake behind the bluff body and also to suppress the vortex shedding phenomena. The Darcy–Brinkman–Forchheimer model has been used for modeling the flow in the porous medium. Effects of Stuart ( N ), Reynolds ( Re ) and Darcy ( Da ) numbers on the flow behavior have been investigated. The results show that the critical Stuart number for suppress vortex shedding decreases with increasing the Darcy numbers. Also, the Stuart number for disappearance the re-circulating wake increases with increased Reynolds number for both porous and solid cylinders. [ABSTRACT FROM AUTHOR]