An efficient Immersed Boundary Method based on penalized direct forcing for simulating flows through arbitrary porous media. The aim of this thesis project is the development of an efficient Immersed Boundary Method (IBM) for simulating Stokes flow through the pores of an arbitrary porous medium. The method is specifically designed to incorporate geometrical data of a porous medium obtained from a Computed Tomography (CT) scanner. The accuracy of the IBM has been determined by a number of benchmark cases of idealized geometries. The geometry of real porous media has been obtained from high resolution micro-CT scans. To validate the simulations of real porous media, a Darcy experiment has been developed to determine the permeability of these porous media. The results show that the IBM can be used to predict the permeability, through Richardson extrapolation of the numerical results, of a real porous medium within an error of 10% of the Darcy experiment and the semi-empirical CarmanKozeny relation.