The IDSA and the homogeneous sphere: Issues and possible improvements

TL;DR

This paper analyzes the IDSA method for radiative transfer in a homogeneous sphere, identifies numerical issues caused by the coupling mechanism, and proposes an improved, more accurate version supported by analytical and numerical evidence.

Contribution

The paper reformulates the IDSA to eliminate numerical difficulties and introduces a new version that improves accuracy in modeling radiative transfer in homogeneous spheres.

Findings

The original IDSA overestimates the streaming component.

Reformulated IDSA avoids numerical difficulties.

New IDSA version is more accurate based on tests.

Abstract

In this paper, we are concerned with the study of the Isotropic Diffusion Source Approximation (IDSA) (Baxter et al., Phys. Rev. E 73, 046118, 2006) of radiative transfer. After having recalled well-known limits of the radiative transfer equation, we present the IDSA and adapt it to the case of the homogeneous sphere. We then show that for this example the IDSA suffers from severe numerical difficulties. We argue that these difficulties originate in the min-max switch coupling mechanism used in the IDSA. To overcome this problem we reformulate the IDSA to avoid the problematic coupling. This allows us to access the modeling error of the IDSA for the homogeneous sphere test case. The IDSA is shown to overestimate the streaming component, hence we propose a new version of the IDSA which is numerically shown to be more accurate than the old one. Analytical results and numerical tests are provided to support the accuracy of the new proposed approximation.