Boltzmann transport equation solver based on phase-point trajectory method for argon gas

Abstract

A method of phase point trajectory (PPT) is presented to solve the Boltzmann transport equation (BTE), which makes it possible to study the time-dependent behaviors of the electron velocity distribution function (EVDF) of ionized gases. The important features of the PPT method are: (a) It is recurrence-free. (b) The governing equations on the phase point trajectories are quite similar to those governing particle dynamics in the particle in cell (PIC) simulation and therefore, the technique is easy to use. (c) It has a unique and cost-effective second-order interpolation scheme. (d) In the PPT method, the full EVDF is calculated (i.e., it is not expanded). In order to illustrate how the PPT method works, the BTE is simulated for argon gas under the influence of an external uniform electric field, and the following are examined as benchmark: (i) Collisionless behaviors of EVDF and (ii) the time-dependent behavior of swarm parameters and their equilibrium values in the presence of elastic and inelastic collisions. (iii) The role of each of the collision terms in the behavior of EVDF and electron density. Finally, it is shown that the results of the PPT simulation are in good agreement with the results of the known relevant simulation methods.