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.