A rational construction of discrete velocity models of the Boltzmann equation
Abstract
A general and effective construction of the collisional operator for the discrete velocity models of the Boltzmann equation is presented. First, definitions of collisions and space of collisional invariants are given, and next a collisional operator with the space of collisional invariants given in advance is constructed. A theorem asserting that every bilinear operator in Euclidean spaces, which has the basic properties of collisional operators, is necessarily of the well known classical form, is demonstrated.
 Publication:

Archiv of Mechanics, Archiwum Mechaniki Stosowanej
 Pub Date:
 1988
 Bibcode:
 1988ArMeS..40..323P
 Keywords:

 Boltzmann Transport Equation;
 Collision Parameters;
 Euclidean Geometry;
 Mathematical Models;
 Energy Conservation;
 Partial Differential Equations;
 Thermodynamics and Statistical Physics