The IDSA and the homogeneous sphere: Issues and possible improvements
For researchers using the IDSA in radiative transfer, this work addresses a specific numerical instability and offers an improved version, though the fix is incremental.
The paper identifies numerical difficulties in the Isotropic Diffusion Source Approximation (IDSA) for radiative transfer in a homogeneous sphere, tracing them to the min-max switch coupling mechanism. A reformulated IDSA is proposed that avoids this coupling and is numerically shown to be more accurate than the original.
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.