Asymptotic approximations to a linear transport equation

Abstract

We put forward three algorithms for computing equations determining asymptotic approximations to solutions of a linear transport equation in the strong scattering asymptote. Applying these algorithms to a one-speed integro-differential linear transport equation in the limit of large scattering cross section, we derive equations that determine various first-, second- and third-order approximations to the scalar flux; one of the first-order approximations satisfies the conventional diffusion equation. We point out a particular diffusion equation that is valid both for large scattering cross sections and for large absorption cross sections.