This work deals with the modelling and simulation of the air bubble injection effect in a water reservoir. The water phase is modelled by a Navier-Stokes quation in which we integrate the air bubble effect by a source term. This one depends on probability density function described by a kinetic model. For the numerical aspects we used particular method for kinetic equation and mixed finite elements method for Navier-Stokes equations. Finally, we present some numercial results to illustrate the used method.