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 - <p style="text-align: justify;">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.</p>