Modelling and Simulations of Moving Droplet in a Rarefied Gas

We study a liquid droplet moving inside a rarefied gas. In other words, we consider a two-phase flow with liquid and rarefied gas phases and an interface between the two phases which deforms with respect to time and space. The gas phase is modelled by the Bhatanager-Gross-Krook (BGK) model of the Boltzmann equation. The liquid phase is modelled by the incompressible Navier-Stokes equations. Interface boundary conditions for the liquid and gas phases are presented. The BGK model is solved by a semi-Lagrangian scheme with a meshfree reconstruction procedure. A similar meshfree particle method is used to solve the incompressible Navier-Stokes equations for the liquid phase. In 1D the solutions of the BGK-Navier-Stokes equations and the Boltzmann-Navier-Stokes equations are compared, where the Boltzmann equation is solved by a direct simulation Monte Carlo method. Results in 1D and 2D physical spaces are presented.