Simulation of a moving liquid droplet inside a rarefied gas region
  We study the dynamics of a liquid droplet inside a gas over a large range of the Knudsen numbers. The moving liquid droplet is modeled by the incompressible Navier-Stokes equations, the surrounding rarefied gas by the Boltzmann equation. The interface boundary conditions between the gas and liquid phases are derived. The incompressible Navier-Stokes equations are solved by a meshfree Lagrangian particle method called Finite Pointset Method (FPM), and the Boltzmann equation by a DSMC type of particle method. To validiate the coupled solutions of the Boltzmann and the incompressible Navier-Stokes equations we have further solved the compressible and the incompressible Navier-Stokes equations in the gas and liquid phases, respectively. In the latter case both the compressible and the incompressible Navier-Stokes equations are also solved by the FPM. In the continuum regime the coupled solutions obtained from the Boltzmann and the incompressible Navier-Stokes equations match with the solutions obtained from the compressible and the incompressible Navier-Stokes equations. In this paper, we presented solutions in one-dimensional physical space. 
Sudarshan Tiwari, Axel Klar, Steffen Hardt
math.NA physics.flu-dyn