Ay. Ender et Ia. Ender, Symmetry of the nonlinear collision operator matrix and new prospects in the moment method for solving the Boltzmann equation, TECH PHYS, 44(9), 1999, pp. 1005-1008
Traditionally, the moment method has been used in kinetic theory to calcula
te transport coefficients. Its application to the solution of more complica
ted problems runs into enormous difficulties associated with calculating th
e matrix elements of the collision operator. The corresponding formulas for
large values of the indices are either lacking or are very cumbersome. In
this paper relations between matrix elements are derived from very general
principles, and these can be employed as simple recurrence relations for ca
lculating all the nonlinear and linear anisotropic matrix elements from ass
igned linear isotropic matrix elements. Efficient programs which implement
this algorithm are developed. The possibility of calculating the distributi
on function out to 8-10 thermal velocities is demonstrated. The results obt
ained open up prospects for solving many topical problems in kinetic theory
. (C) 1999 American Institute of Physics. [S1063-7842(99)00209-3].