Two Uniform Tailored Finite Point Schemes for the Two Dimensional Discrete Ordinates Transport Equations with Boundary and Interface Layers release_fjrwqvxstredtkkzhmtl3pw7jm

by Houde Han, Min Tang, Wenjun Ying

Published in Communications in Computational Physics by Global Science Press.

Volume 15, Issue 03 p797-826 (2014)


<jats:title>Abstract</jats:title>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.
In application/xml+jats format

Archived Files and Locations

application/pdf  1.2 MB
file_fargebrcanbzzcxictpaspsbxa (web) (webarchive)
Read Archived PDF
Type  article-journal
Stage   published
Year   2014
Language   en ?
Container Metadata
Not in DOAJ
In Keepers Registery
ISSN-L:  1815-2406
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 3e3f6804-1e88-4901-a03d-ac34820b93fa