Traditionally, people in the Mediterranean region knew that the temperatures in their courtyards were cooler in summer than outside temperature. This paper provides a quantitative study on the usefulness of Mediterranean courtyards as passive energy saving systems. This work is based on the creation of a Computational Fluid Dynamics (CFD) numerical model developed using the open source Freefem++ language. In this work, first the numerical model is tested using simplified-shape courtyards which have been previously studied both physically under controlled parameters, and mathematically through numerical simulations. We also study the most appropriate depth ratio for a courtyard, based on these simplified shapes, depending on the climate. Secondly, we apply the numerical model in a real geometry, the Monte Málaga hotel. We compare the numerical results with the monitored data of the temperature in the courtyard of the hotel. The numerical model takes into account precomputed solar radiation in the walls of the courtyard, the predominant wind and buoyancy effects.