Projection method for Boltzmann energy equations

Abstract

The Boltzmann equation for a dilute spatially homogeneous gas —wherein the scattering is isotropic—is considered. It is shown that the equation can be projected into a Hilbert space, resulting in an autonomous differential system which, from a computational point of view, is very appealing. Conservation laws are automatically obeyed; and, for models with isotropic cross-sections depending on the energy with a power law, the requisite matrix elements can be analytically evaluated as finite sums of products of gamma-functions.