Diffusive Corrections to Pn Approximations

TL;DR

This paper introduces a diffusive correction to Pn approximations for radiative transfer, derived from an operator-based theoretical framework, and validates it through numerical experiments in multiple dimensions.

Contribution

It develops the Dn approximation, a novel diffusive correction to Pn methods, based on an operator formulation, enhancing accuracy in moment method applications.

Findings

The Dn approximation improves Pn accuracy in numerical tests.

Numerical validation in 1D and 2D demonstrates the effectiveness of the correction.

The operator approach provides a systematic way to derive moment closure corrections.

Abstract

In this paper, we investigate moment methods from a general point of view using an operator notation. This theoretical approach lets us explore the moment closure problem in more detail. This gives rise to a new idea, proposed in [Levermore2005, Levermore2009], of how to improve the well-known Pn approximations. We systematically develop a diffusive correction to the Pn equations from the operator formulation - the so-called Dn approximation. We validate the new approach with numerical examples in one and two dimensions.