Research & Teaching Faculty

Maple code for the calculation of the matrix elements of the Boltzmann collision operators for mixtures.

TitleMaple code for the calculation of the matrix elements of the Boltzmann collision operators for mixtures.
Publication TypeJournal Article
Year of Publication2010
AuthorsShizgal, BD, Dridi, R
JournalComputer Physics Communications
Volume181
Pagination1633 - 1640
Date Published2010///
ISBN Number0010-4655
Keywordsgaseous mixt Boltzmann collision operator matrix element Maple code
Abstract

A Maple code is provided which is used to compute the matrix elements of the collision operators in the Boltzmann equation for arbitrary differential elastic collision cross section. The present paper describes an efficient method for the calcn. of the matrix elements of the collision operators in the Sonine basis set. The method employs the generating functions for these polynomials. The transport properties of gaseous mixts. of atoms and/or ions are generally detd. from solns. of the Boltzmann equation. The soln. of the Boltzmann equation for the velocity distribution functions requires a representation of the integral collision operators defined by the differential cross sections describing collisions between pairs of particles. Many applications have considered either the simple hard sphere cross section or the cross section corresponding to the inverse fourth power of the inter-particle distance ("Maxwell mols."). There are a few applications where realistic quantum mech. cross sections have been used. The basis set of Sonine (or Laguerre) polynomials is the basis set of choice used to represent the distribution functions. The Maple code provided is used to express the matrix elements of the collision operators in terms of a finite sum of the omega integrals of transport theory and defined by the differential cross section. Thus the matrix representations of the collision operators are applicable to arbitrary interaction potentials. [on SciFinder(R)]