Effects of exit boundary conditions on results of kinetic simulations of spherical expansion of mon- and diatomic gases in a gravitational field

Abstract

The spherical expansion of mon- and diatomic gases in a spherically symmetric gravitational field is studied in kinetic simulations. The simulations are performed with the direct simulation Monte Carlo (DSMC) method in the range of the source Knudsen number, the ratio of the mean free path of gas molecules to the source radius, from 0.01 to 0.001, and in the range of the source Jeans parameter, the ratio of the characteristic gravitational binding energy of a gas molecule to its thermal energy, from 0 to 6. The exit boundary position R1 of the computational domain was varied from 10 to 800 times the source radii R0 in order to quantify the effect of the size of the computational domain and kinetic escape boundary conditions on the flow structure and escape rates. It is shown that the flow structure and escape rates for both mon- and diatomic gases are highly sensitive to the position of the exit boundary, when the source Knudsen number is sufficiently small and the source Jeans parameter corresponds to the transition from blow-off to Jean-like thermal escape. Outside the transitional range, the flow structures and escape rates are only marginally affected by the position of the exit boundary. In the case of a diatomic gas, the calculated flow structures converge with increasing size of the computational domain. In the case of a monatomic gas, the flow structures calculated for the transitional range of the Jeans parameter do not exhibit convergence with respect to increasing size of the computational domain in the considered range of R1/R0. It is shown that such flows remain subsonic and retain local equilibrium at arbitrary large distances from the source. The solution of the kinetic problem for a given molecular model in these conditions is uniquely defined by three parameters including the source Jeans parameter and Knudsen number and an additional parameter that constrains the flow far downstream. This additional parameter can be chosen in the form of the imposed number escape rate.