A hybrid kinetic/fluid model for solving the gas dynamics Boltzmann–BGK equation

Our purpose is to derive a hybrid model for particle systems which combines a kinetic description of the fast particles with a fluid description of the thermal ones. In the present work, fast particles will be described through a collisional kinetic equation of Boltzmann–BGK type while thermal particles will be modeled by means of a system of Euler type equations. Then, we construct a numerical scheme for this model. This scheme satisfies exact conservation properties. We validate the approach by presenting various numerical tests.