Coupled solution of the Boltzmann and Navier–Stokes equations in gas–liquid two phase flow

Abstract

We study gas–liquid two-phase flow over a large range of Knudsen numbers inside the gase phase. The liquid phase is modeled by the incompressible Navier–Stokes equations, the gas phase by the Boltzmann equation, allowing to consider rarefied conditions inside the gas. 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 validate 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.