Volume 15, Issue 3
Two Uniform Tailored Finite Point Schemes for the Two Dimensional Discrete Ordinates Transport Equations with Boundary and Interface Layers

Houde Han, Min Tang & Wenjun Ying

Commun. Comput. Phys., 15 (2014), pp. 797-826.

Published online: 2014-03

Preview Full PDF 147 1041
Export citation
  • Abstract

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 nodecentered 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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-15-797, author = {}, 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 = {

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 nodecentered 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.130413.010813a}, url = {http://global-sci.org/intro/article_detail/cicp/7116.html} }
TY - JOUR T1 - Two Uniform Tailored Finite Point Schemes for the Two Dimensional Discrete Ordinates Transport Equations with Boundary and Interface Layers JO - Communications in Computational Physics VL - 3 SP - 797 EP - 826 PY - 2014 DA - 2014/03 SN - 15 DO - http://dor.org/10.4208/cicp.130413.010813a UR - https://global-sci.org/intro/article_detail/cicp/7116.html KW - AB -

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 nodecentered 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.

Houde Han, Min Tang & Wenjun Ying. (2020). Two Uniform Tailored Finite Point Schemes for the Two Dimensional Discrete Ordinates Transport Equations with Boundary and Interface Layers. Communications in Computational Physics. 15 (3). 797-826. doi:10.4208/cicp.130413.010813a
Copy to clipboard
The citation has been copied to your clipboard