The IDSA and the homogeneous sphere: Issues and possible improvements

Abstract

In this paper, we are concerned with the study of the Isotropic Diffusion Source Approximation (IDSA) [6] 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. 4 JÉRÔME MICHAUD 2.2. Reaction limit. The reaction regime is a special limit of the diffusion limit in which the total opacity κ is so large that the diffusion term can be dropped in Eq. (9). This corresponds to the following closure relationsThe corresponding evolution equation readswhere we defined the reaction evolution operator L reac J for J as before. The reaction limit is valid in regions where the mean free path κ −1 is negligible compared with the typical length scale of the system. As for the diffusion limit, one can use asymptotic expansion with a different scaling in order to derive this limit, see for example [2]. 6 JÉRÔME MICHAUD with g idsa := h free . Comparing this closure relations with the asymptotic limits described in Section 2, we have the following operator definitions L t J := L reac J Received xxxx 20xx; revised xxxx 20xx.