In this work, we are interested in a complex fluid-kinetic model that aims to take into account the compressibility of the droplets of the spray. The ambient fluid is described by Euler-like equations, in which the transfer of momentum and energy form the droplets is taken into account, while the spray is represented by a probability density function satisfying a Vlasov-like equation. Implicit terms crop up because of the compressibility of the droplets. After having derived the model, we prove that golbal conservations are satisfied. Then we present two numerical tests. The first one enables us to validate the numerical code, while the second one is performed in a physically realistic situation.
"A Modeling of Compressible Droplets in a Fluid." Commun. Math. Sci. 1 (4) 657 - 669, December 2003.