Equilibrium and non-equilibrium diffusion approximation for the radiative transfer equation
Year: 2025
Type: article
Abstract: In this paper, we study the distribution of the temperature within a body where the heat is transported only by radiation. Specifically, we consider the situation where both emission-absorption and scattering processes take place. We study the initial-boundary value problem given by the coupling of the radiative transfer equation with the energy balance equation on a convex domain normal upper Omega subset of double struck upper R cubed Ω ⊂ R 3 $ \Omega \subset {\mathbb{R}}^3$ in the diffusion approximation regime, that is, when the mean free path of the photons tends to zero. Using the method of matched asymptotic expansions, we will derive the limit initial-boundary value problems for all different possible scaling limit regimes, and we will classify them as equilibrium or non-equilibrium diffusion approximation. Moreover, we will observe the formation of boundary and initial layers for which suitable equations are obtained. We will consider both stationary and time-dependent problems as well as different situations in which the light is assumed to propagate either instantaneously or with finite speed.
Authors: Elena Demattè, Juan J. L. Velázquez
Institution: University of Bonn
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W4414479201