PreprintarXiv licencearXiv
A Robust High-order Approximation of the Gray Thermal Radiative Transfer Equations
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.
Related
- On a boundary value problem related to radiative heat transfer
- Radiative Vlasov-Maxwell Equations
- Long-Time Behavior towards Generic Riemann Solutions for Radiative Euler Equations
- Low-rank SI-DSA and GMRES-DSA for Radiative Transfer Equation with Adaptive Accuracy Control
- Generalized Stochastic Approximation of the Log-Likelihood Ratio for Robust Sequential Change-Point Detection
BibTeX
@misc{guermond2026robust,
title = {{A Robust High-order Approximation of the Gray Thermal Radiative Transfer Equations}},
author = {Jean-Luc Guermond and Wyatt M. R. Smith and Eric J. Tovar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41967},
eprint = {2610.41967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41967},
}
RIS
TY - UNPB
TI - A Robust High-order Approximation of the Gray Thermal Radiative Transfer Equations
AU - Jean-Luc Guermond
AU - Wyatt M. R. Smith
AU - Eric J. Tovar
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41967
UR - https://arxiv.org/abs/2610.41967
AB - 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.
ER -