The objective of the work presented here was to develop a numerical model for simulating sound propagation in a confined environment while accurately taking account of the acoustic scattering and diffraction effects generated by the presence of geometrical relief on the room surfaces. To achieve this, two methods were combined: the Adaptive Rectangular Decomposition (ARD) method, for simulating the propagation in the enclosed space, and the Finite-Difference Time-Domain (FDTD) method, for accurately modelling the complex boundaries of the room being studied. Firstly, this paper presents a way of improving how account is taken of the Perfectly Matched Layers (PMLs) used to simulate absorption of the waves at the boundaries of the domain. It then describes in detail the method of creating Digital Impedance Filters (DIFs) and the way in which they were incorporated into the ARD method in order to simulate surfaces having relief and that are characterized by frequency-dependent impedance. The model was then compared with theoretical results obtained using the Kobayashi Potential (KP) method and with measurements of the reflected pressure field above a surface containing rectangular cavities under semi-anechoic conditions. Finally, another application of the numerical model was implemented in a real room delimited by surfaces having geometrical relief.