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Volume 27, Issue 4
An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation

Min Zhang, Juan Cheng, Weizhang Huang & Jianxian Qiu

DOI: 10.4208/cicp.OA-2018-0317

Commun. Comput. Phys., 27 (2020), pp. 1140-1173.

Published online: 2020-02

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  • Abstract

The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time, frequency, space and angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needs to handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions. Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinate method for angular discretization. The former employs a dynamic mesh adaptation strategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency are demonstrated in a selection of one- and two-dimensional numerical examples.

  • Keywords

Adaptive moving mesh, discontinuous Galerkin method, radiative transfer equation, high order accuracy, high resolution.

  • AMS Subject Headings

65M50, 65M60, 65M70, 65R05, 65.75

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

minzhang2015@stu.xmu.edu.cn (Min Zhang)

cheng juan@iapcm.ac.cn (Juan Cheng)

whuang@ku.edu (Weizhang Huang)

jxqiu@xmu.edu.cn (Jianxian Qiu)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-1140, author = {Zhang , MinCheng , JuanHuang , Weizhang and Qiu , Jianxian}, title = {An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation}, journal = {Communications in Computational Physics}, year = {2020}, volume = {27}, number = {4}, pages = {1140--1173}, abstract = {

The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time, frequency, space and angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needs to handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions. Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinate method for angular discretization. The former employs a dynamic mesh adaptation strategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency are demonstrated in a selection of one- and two-dimensional numerical examples.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0317}, url = {http://global-sci.org/intro/article_detail/cicp/14830.html} }
TY - JOUR T1 - An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation AU - Zhang , Min AU - Cheng , Juan AU - Huang , Weizhang AU - Qiu , Jianxian JO - Communications in Computational Physics VL - 4 SP - 1140 EP - 1173 PY - 2020 DA - 2020/02 SN - 27 DO - http://doi.org/10.4208/cicp.OA-2018-0317 UR - https://global-sci.org/intro/article_detail/cicp/14830.html KW - Adaptive moving mesh, discontinuous Galerkin method, radiative transfer equation, high order accuracy, high resolution. AB -

The radiative transfer equation models the interaction of radiation with scattering and absorbing media and has important applications in various fields in science and engineering. It is an integro-differential equation involving time, frequency, space and angular variables and contains an integral term in angular directions while being hyperbolic in space. The challenges for its numerical solution include the needs to handle with its high dimensionality, the presence of the integral term, and the development of discontinuities and sharp layers in its solution along spatial directions. Its numerical solution is studied in this paper using an adaptive moving mesh discontinuous Galerkin method for spatial discretization together with the discrete ordinate method for angular discretization. The former employs a dynamic mesh adaptation strategy based on moving mesh partial differential equations to improve computational accuracy and efficiency. Its mesh adaptation ability, accuracy, and efficiency are demonstrated in a selection of one- and two-dimensional numerical examples.

Zhang , MinCheng , JuanHuang , Weizhang and Qiu , Jianxian. (2020). An Adaptive Moving Mesh Discontinuous Galerkin Method for the Radiative Transfer Equation. Communications in Computational Physics. 27 (4). 1140-1173. doi:10.4208/cicp.OA-2018-0317
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