TY - JOUR
T1 - A Sparse Grid Discrete Ordinate Discontinuous Galerkin Method for the Radiative Transfer Equation
AU - Huang , Jianguo
AU - Yu , Yue
JO - Communications in Computational Physics
VL - 4
SP - 1009
EP - 1036
PY - 2021
DA - 2021/08
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0248
UR - https://global-sci.org/intro/article_detail/cicp/19392.html
KW - Radiative transfer equation, sparse grid method, discrete ordinate method, discontinuous Galerkin method.
AB - <p style="text-align: justify;">The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case,
leading to great difficulties in numerical simulation. To tackle this bottleneck, we first
use the discrete ordinate technique to discretize the scattering term, an integral with respect to the angular variables, resulting in a semi-discrete hyperbolic system. Then, we
make the spatial discretization by means of the discontinuous Galerkin (DG) method
combined with the sparse grid method. The final linear system is solved by the block
Gauss-Seidal iteration method. The computational complexity and error analysis are
developed in detail, which show the new method is more efficient than the original
discrete ordinate DG method. A series of numerical results are performed to validate
the convergence behavior and effectiveness of the proposed method.</p>