Half-space Problem for Linearized ES-BGK Model Equation with Unsteady Evaporation and Condensation Flows

We consider time-periodic gas flows on the basis of the ellipsoidal-statistical Bhatnager-Gross-Krook (ES-BGK) model equation in a semi-infinite expanse of an initially equilibrium monatomic gas bounded by its planar condensed phase. The kinetic boundary condition at the vapor-liquid interface is assumed to be the complete condensation condition with periodically time-varying macroscopic variables (temperature, saturated vapor density and velocity of the interface), and the boundary condition at infinity is the local equilibrium distribution function. The time scale of variation of macroscopic variables is assumed to be much larger than the mean free time of gas molecules, and the variations of those from a reference state are assumed to be sufficiently small. We numerically investigate thus formulated time-dependent half-space problem for the linearized ES-BGK model equation with the finite difference method. As a result, we found that the mass flux at the interface is not in phase with the difference between the velocity at infinity and the velocity of interface for the case where the Strouhal number is not equal to zero.