On a Vlasov equation model for two-phase fluid flow

We consider the problem of water–air two-phase flow, which occurs during water aeration by air injection. We present and analyze a new model incorporating a nonlocal boundary condition, integrating the effect of the air phase through a source term applied to the water phase. This term is described using a kinetic approach based on the Vlasov equation. A numerical study is conducted, and numerical experiments are presented to demonstrate the effectiveness of the presented model