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

Published online by Cambridge University Press:  03 June 2015

Houde Han*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Haidian, Beijing 100084, P.R. China
Min Tang*
Affiliation:
Department of Mathematics, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, Minhang, Shanghai 200240, P.R. China
Wenjun Ying*
Affiliation:
Department of Mathematics, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, Minhang, Shanghai 200240, P.R. China
*Corresponding
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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 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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2014

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