Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet

A. S. Arkhipov ; A. M. Bishaev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 10, pp. 1904-1925

Résumé

A numerical method is constructed for solving the system of kinetic equations describing the behavior of a rarefied plasma jet exhausted from a Hall thruster. A similar problem was previously considered in the steady case. Now the same problem is solved in the unsteady formulation. The numerical method is based on a generalization of the splitting method with respect to physical processes, which is widely used in rarefied gas dynamics. The basic difficulty faced in the natural generalization of this method as applied to thruster jets is that a boundary condition has to be taken into account when the ion distribution function is determined. This difficulty is overcome by analytically selecting the corresponding term at the stage of free-molecular motion. Another difficulty that can be coped with by the splitting method is that the ion and neutral velocity spaces have widely different scales. Techniques for making the method conservative are described, and situations in which this is necessary are discussed. Qualitative characteristics of some numerical computations are compared with experimental data. The comparison shows that the numerical method constructed adequately reproduces the behavior of the modeled object.