A Corrected HNT-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

doi:10.1007/s42967-024-00376-z

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (2): 689-717.doi: 10.1007/s42967-024-00376-z

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A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

Song Jiang¹, Qi Li¹, Wenjun Sun^1,2

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

收稿日期:2023-07-27 修回日期:2024-01-13 接受日期:2024-01-20 出版日期:2025-06-20 发布日期:2025-04-21
通讯作者: Wenjun Sun,sun_wenjun@iapcm.ac.cn;Song Jiang,jiang@iapcm.ac.cn;Qi Li,qili1725535699@163.com E-mail:sun_wenjun@iapcm.ac.cn;jiang@iapcm.ac.cn;qili1725535699@163.com
基金资助:
The current research is supported by the National Key R & D Program (Grant no. 2020YFA0712200) and the Sino-German Science Center (Grant no. GZ 1465) for Jiang, and by the Beijing Natural Science Foundation of China (Grant no. Z230003) and the NSFC (Grant nos. 12292981, 12292982) for Sun.

A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

Song Jiang¹, Qi Li¹, Wenjun Sun^1,2

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

Received:2023-07-27 Revised:2024-01-13 Accepted:2024-01-20 Online:2025-06-20 Published:2025-04-21
Supported by:
The current research is supported by the National Key R & D Program (Grant no. 2020YFA0712200) and the Sino-German Science Center (Grant no. GZ 1465) for Jiang, and by the Beijing Natural Science Foundation of China (Grant no. Z230003) and the NSFC (Grant nos. 12292981, 12292982) for Sun.

摘要/Abstract

摘要： In this paper, the corrected method to the original H_N^T-unified gas kinetic scheme (H_N^T-UGKS) is developed in order to solve the nonlinear radiative transfer equations with boundary layers. The H_N^T-UGKS is an asymptotic preserving (AP) scheme that uses UGKS for spatial discretization and the hybrid H_N^T method for angular discretization which is constructed in the paper (Li et al. in Nucl. Sci. Eng. 198(5): 993–1020, 2024). First, the correction idea in Mieussens (J. Comput. Phys. 253: 138–156, 2013) is adopted, such that H_N^T-UGKS can correctly simulate the linear radiative transfer equation with boundary layers. Then, for the nonlinear radiative transfer equations with boundary layers, the transformation from the implicit Monte Carlo (IMC) method is introduced to rewrite the nonlinear transfer equations into a linearized system. It is the key point in the construction of the current scheme to use this linearized system to construct the numerical boundary fluxes. In this way, the boundary density is included in the numerical fluxes, and consequently, the modification method for the linear radiative transfer equation can be used to deal with the nonlinear problem studied in this paper. A number of numerical examples are presented to demonstrate the accuracy and effectiveness of the current scheme for resolving boundary layers in both linear and nonlinear radiative transfer problems.

关键词: Nonlinear radiative transfer, Boundary layer, H_N^T-UGKS, Implicit Monte Carlo (IMC) method

Abstract: In this paper, the corrected method to the original H_N^T-unified gas kinetic scheme (H_N^T-UGKS) is developed in order to solve the nonlinear radiative transfer equations with boundary layers. The H_N^T-UGKS is an asymptotic preserving (AP) scheme that uses UGKS for spatial discretization and the hybrid H_N^T method for angular discretization which is constructed in the paper (Li et al. in Nucl. Sci. Eng. 198(5): 993–1020, 2024). First, the correction idea in Mieussens (J. Comput. Phys. 253: 138–156, 2013) is adopted, such that H_N^T-UGKS can correctly simulate the linear radiative transfer equation with boundary layers. Then, for the nonlinear radiative transfer equations with boundary layers, the transformation from the implicit Monte Carlo (IMC) method is introduced to rewrite the nonlinear transfer equations into a linearized system. It is the key point in the construction of the current scheme to use this linearized system to construct the numerical boundary fluxes. In this way, the boundary density is included in the numerical fluxes, and consequently, the modification method for the linear radiative transfer equation can be used to deal with the nonlinear problem studied in this paper. A number of numerical examples are presented to demonstrate the accuracy and effectiveness of the current scheme for resolving boundary layers in both linear and nonlinear radiative transfer problems.

Key words: Nonlinear radiative transfer, Boundary layer, H_N^T-UGKS, Implicit Monte Carlo (IMC) method

中图分类号:

Song Jiang, Qi Li, Wenjun Sun. A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations[J]. Communications on Applied Mathematics and Computation, 2025, 7(2): 689-717.

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A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

A Corrected H_N^T-UGKS for Boundary Layer Problems of the Gray Radiative Transfer Equations

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