This work is a contribution to the numerical modeling of suspension system in the kinetic theory framework. This continuum description of suspension system allows to account for the microstructure impact on the kinetic of the macroscopic flow. However, its main drawback is related to the high dimensional spaces in which kinetic theory models are defined and makes difficult for classical deterministic approaches to solve such systems. One possibility for circumventing, or at least alleviate, the weight of the micro-macro kinetic theory approaches lies in the use of separated representations strategies based on the Proper Generalized Decomposition (PGD). A study of different PGD algorithms is driven, illustrating the efficiency of these algorithms in terms of convergence speed and optimality of the solution obtained. The immiscible fluids blends modeling is driven using the area tensor which is a powerful numerical tool for characterizing blends. However it needs the introduction of closure relation of which impact is measured using equivalent and exact kinetic theory model. Finally, the numerical modeling of colloidal suspension system described by the Smoluchowski equation presents an original approach of the modeling of solid suspension system. This description allows to circumvent the statistical noise inherent to the stochastic approaches commonly used.
