The Non-Classical Boltzmann Equation, and Diffusion-Based Approximations to the Boltzmann Equation

Abstract

We show that several diffusion-based approximations (classical diffusion or SP1, SP2, SP3) to the linear Boltzmann equation can (for an infinite, homogeneous medium) be represented exactly by a non-classical transport equation. As a consequence, we indicate a method to solve diffusion-based approximations to the Boltzmann equation via Monte Carlo, with only statistical errors - no truncation errors.

16 pages, 3 figures

References in corpus (3)

• Non-classical transport with angular-dependent path-length distributions. 1: Theory
• Non-classical transport with angular-dependent path-length distributions. 2: Application to pebble bed reactor cores
• Rigorous asymptotic and moment-preserving diffusion approximations for generalized linear Boltzmann transport in arbitrary dimension

Cited by in corpus (5)

• A reciprocal formulation of non-exponential radiative transfer. 1: Sketch and motivation
• A Reciprocal Formulation of Nonexponential Radiative Transfer. 2: Monte Carlo Estimation and Diffusion Approximation
• The Nonclassical Diffusion Approximation to the Nonclassical Linear Boltzmann Equation
• Nonclassical Particle Transport in 1-D Random Periodic Media
• On the Application of the Analytical Discrete Ordinates Method to the Solution of Nonclassical Transport Problems in Slab Geometry