A Numerical Method of Solution of the Boltzmann Equation in a Weakly Ionized Heterogeneous Gas
Abstract
We give a numerical method of solution of the Boltzmann equation for a weakly ionized gas based on the study of the characteristic curves defined by the free motion of particles. First, we perform a systematic study of the topological properties of these characteristic lines when collisions are present. We show that their distribution not only gives us a method of attack for the numerical resolution but also allows us to predict, even before solving the Boltzmann equation, the complete behavior of the distribution function. Second, we define several discrete schemes and we prove that they are convergent and stable. We also give a brief proof of the convergence of the iterative process associated with the resolution of the discrete linear system of equations. Finally, we give the results obtained for helium gas, both the transmission factor of electrons and the isotropic part of the distribution function. The main feature to be emphasized is the existence of a distribution presenting a shape with a succession of "knobs" and "hollows" characteristic of a nonequilibrium state.
 Publication:

Journal of Computational Physics
 Pub Date:
 May 1977
 DOI:
 10.1016/00219991(77)901097
 Bibcode:
 1977JCoPh..24...43S
 Keywords:

 Boltzmann Transport Equation;
 Collisional Plasmas;
 Electron Distribution;
 Ionized Gases;
 Iterative Solution;
 Particle Motion;
 Approximation;
 Convergence;
 Distribution Functions;
 Electron Scattering;
 Nonuniform Plasmas;
 Plasma Physics