@Article{CiCP-15-797,
author = {Houde Han, Min Tang and Wenjun Ying},
title = {Two Uniform Tailored Finite Point Schemes for the Two Dimensional Discrete Ordinates Transport Equations with Boundary and Interface Layers},
journal = {Communications in Computational Physics},
year = {2014},
volume = {15},
number = {3},
pages = {797--826},
abstract = {<p style="text-align: justify;">This paper presents two uniformly convergent numerical schemes for the
two dimensional steady state discrete ordinates transport equation in the diffusive
regime, which is valid up to the boundary and interface layers. A five-point node-centered and a four-point cell-centered tailored finite point schemes (TFPS) are introduced. The schemes first approximate the scattering coefficients and sources by piecewise constant functions and then use special solutions to the constant coefficient equation as local basis functions to formulate a discrete linear system. Numerically, both
methods can not only capture the diffusion limit, but also exhibit uniform convergence
in the diffusive regime, even with boundary layers. Numerical results show that the
five-point scheme has first-order accuracy and the four-point scheme has second-order
accuracy, uniformly with respect to the mean free path. Therefore, a relatively coarse
grid can be used to capture the two dimensional boundary and interface layers.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.130413.010813a},
url = {http://global-sci.org/intro/article_detail/cicp/7116.html}
}