It is necessary to adapt existing models in order to simulate the number concentration, and correctly account for nanoparticles, in both free and confined atmospheres. A model of particle dynamics capable of following accurately the number as well as the mass concentration of particles, with an optimal calculation time, has been developed. The dynamics of particles depends on various processes, the most important ones being condensation/evaporation, followed by nucleation, coagulation, and deposition phenomena. These processes are well-known for fine and coarse particles, but some additional phenomena must be taken into account when applied to nanoparticles, such as the Kelvin effect for condensation/evaporation and the van der Waals forces for coagulation. This work focused first on condensation/evaporation, which is the most numerically challenging process. Particles were assumed to be of spherical shape. The Kelvin effect has been taken into account as it becomes significant for particles with diameter below 50 nm. The numerical schemes are based on a sectional approach : the particle size range is discretized in sections characterized by a representative diameter. A redistribution algorithm is used, after condensation/ evaporation occurred, in order to keep the representative diameter between the boundaries of the section. The redistribution can be conducted in terms of mass or number. The key point in such algorithms is to choose which quantity has to be redistributed over the fixed sections. We have developed a hybrid algorithm that redistributes the relevant quantity for each section. This new approach has been tested and shows significant improvements with respect to most existing models over a wide range of conditions. The process of coagulation for nanoparticles has also been solved with a sectional approach. Coagulation is monitored by the brownian motion of nanoparticles. This approach is shown to be more efficient if the coagulation rate is evaluated using the representative diameter of the section, rather than being integrated over the whole section. Simulations also reveal that the van derWaals interactions greatly enhance coagulation of nanoparticles. Nucleation has been incorporated into the newly developed model through a direct source of nanoparticles in the first size section, beginning at one nanometer. The formulation of this rate of nucleation corresponds to that of sulfuric acid but the treatment of the numerical interactions between nucleation, coagulation and condensation/evaporation is generic. Various strategies aiming to solve separately or jointly these three processes are discussed. In order to provide recommendations, several numerical splitting methods have been implemented and evaluated regarding their CPU times and their accuracy in terms of number and mass concentrations
