A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS

doi:10.1007/s10473-025-0604-x

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (6): 2391-2420.doi: 10.1007/s10473-025-0604-x

A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS

Qi LI¹, Wenjun SUN, Song JIANG^2,*

1. Beijing Computational Science Research Center, Beijing 100193, China;
2. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
3. Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China

收稿日期:2025-01-31 修回日期:2025-07-16 出版日期:2025-11-25 发布日期:2025-11-14

A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS

Qi LI¹, Wenjun SUN, Song JIANG^2,*

1. Beijing Computational Science Research Center, Beijing 100193, China;
2. National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
3. Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China

Received:2025-01-31 Revised:2025-07-16 Online:2025-11-25 Published:2025-11-14
Contact: ^*Song JIANG, E-mail: jiang@iapcm.ac.cn
About author:Qi LI, E-mail: qili1725535699@163.com; Wenjun SUN, E-mail: wjsun@amss.ac.cn
Supported by:
Beijing Natural Science Foundation (Z230003) for Sun, and by the National Key R&D Program (2020YFA0712200), the National Key Project (GJXM92579) and the Sino-German Science Center (GZ 1465) for Jiang.

摘要/Abstract

摘要： This paper extends the previous work [1] for the three-temperature gray radiative transfer equations to the frequency-dependent case. Since the additional frequency variable is considered, the equations are more complicated than those in the gray case. Moreover, opacity may be typically a decreasing function of the frequency variable in applications. At the same spatial location, the equations can be in the optically thick case for low frequency photons, while in the optically thin case for high frequency ones. Thus, the resulting discrete equations can significantly increase the computational cost for opacity having the multi-scale property in multiple frequency radiation. Due to the presence of the radiation-electron coupling, electron-ion coupling, and electron-ion diffusion terms, the model under consideration exhibits strong nonlinearity and strong coupling properties. In this paper, the multigroup method is used to discretize the frequency variable and the $H^T_N$ method to discretize the angular variable first. Then, within the framework of a unified gas kinetic scheme (UGKS), a multigroup $H^T_N$-UGKS method is constructed to solve this complex model iteratively. Furthermore, it can be shown that as the Knudsen number tends to zero, with variations in the electron-ion coupling, absorption, and scattering coefficients, the multigroup $H^T_N$-UGKS scheme can converge to numerical schemes for the single-temperature, two-temperature, and the frequency-dependent three-temperature, two-temperature diffusion limit equations, respectively. Finally, several numerical examples are provided to validate the effectiveness and stability of the proposed scheme.

关键词: frequency-dependent radiative transfer, three-temperature model, $H^T_N$ method, unified gas kinetic scheme, asymptotic preserving property

Abstract: This paper extends the previous work [1] for the three-temperature gray radiative transfer equations to the frequency-dependent case. Since the additional frequency variable is considered, the equations are more complicated than those in the gray case. Moreover, opacity may be typically a decreasing function of the frequency variable in applications. At the same spatial location, the equations can be in the optically thick case for low frequency photons, while in the optically thin case for high frequency ones. Thus, the resulting discrete equations can significantly increase the computational cost for opacity having the multi-scale property in multiple frequency radiation. Due to the presence of the radiation-electron coupling, electron-ion coupling, and electron-ion diffusion terms, the model under consideration exhibits strong nonlinearity and strong coupling properties. In this paper, the multigroup method is used to discretize the frequency variable and the $H^T_N$ method to discretize the angular variable first. Then, within the framework of a unified gas kinetic scheme (UGKS), a multigroup $H^T_N$-UGKS method is constructed to solve this complex model iteratively. Furthermore, it can be shown that as the Knudsen number tends to zero, with variations in the electron-ion coupling, absorption, and scattering coefficients, the multigroup $H^T_N$-UGKS scheme can converge to numerical schemes for the single-temperature, two-temperature, and the frequency-dependent three-temperature, two-temperature diffusion limit equations, respectively. Finally, several numerical examples are provided to validate the effectiveness and stability of the proposed scheme.

Key words: frequency-dependent radiative transfer, three-temperature model, $H^T_N$ method, unified gas kinetic scheme, asymptotic preserving property

中图分类号:

65M08

Qi LI, Wenjun SUN, Song JIANG. A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS[J]. 数学物理学报(英文版), 2025, 45(6): 2391-2420.

Qi LI, Wenjun SUN, Song JIANG. A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS[J]. Acta mathematica scientia,Series B, 2025, 45(6): 2391-2420.

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A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS

A $H^T_N$-UGKS SCHEME FOR THE THREE-TEMPERATURE FREQUENCY-DEPENDENT RADIATIVE TRANSFER EQUATIONS

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