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arXiv · 2610.41967

A Robust High-order Approximation of the Gray Thermal Radiative Transfer Equations

Jean-Luc Guermond·Wyatt M. R. Smith·Eric J. Tovar
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Abstract

We present a high-order, positivity preserving, and asymptotic preserving approximation of the gray radiative transfer equations. The time and space approximation is done using a diagonally-implicit Runge-Kutta method with stabilized, continuous finite elements, and the angular approximation uses the method of discrete ordinates. We detail a simple and robust inner/outer iteration strategy to solve these equations and prove that the proposed scheme is exactly conservative, independent of iterative tolerances. A maximum and minimum principle is enforced using a conservative redistribution limiting technique, and the method is demonstrated to be robust in the thick diffusion limit.

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Jean-Luc Guermond, Wyatt M. R. Smith, Eric J. Tovar. 2026-10-30. A Robust High-order Approximation of the Gray Thermal Radiative Transfer Equations. https://arxiv.org/abs/2610.41967

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