This paper deals with the build-up of concentration when a continuous source of helium is supplied in an air-filled enclosure. Our aim is to reproduce the results of a small-scale experimental study ([11]). To begin with, the size of the experiment is reduced from 1/10 to 3/5 for the present analysis. Hypotheses are made in order to reduce the dimension of the real problem. Numerical simulations are carried out on fine grids without any turbulence modeling. The flow structure and the concentration profile of the resulting flow are analyzed and compared with theoretical results.