A Uniform First-Order Method for the Discrete Ordinate Transport Equation with Interfaces in X,Y-Geometry
Year: 2009
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 6 : pp. 764–786
Abstract
A uniformly first-order convergent numerical method for the discrete-ordinate transport equation in the rectangle geometry is proposed in this paper. Firstly we approximate the scattering coefficients and source terms by piecewise constants determined by their cell averages. Then for each cell, following the work of De Barros and Larsen [1, 19], the solution at the cell edge is approximated by its average along the edge. As a result, the solution of the system of equations for the cell edge averages in each cell can be obtained analytically. Finally, we piece together the numerical solution with the neighboring cells using the interface conditions. When there is no interface or boundary layer, this method is asymptotic-preserving, which implies that coarse meshes (meshes that do not resolve the mean free path) can be used to obtain good numerical approximations. Moreover, the uniform first-order convergence with respect to the mean free path is shown numerically and the rigorous proof is provided.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2009.09-m2894
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 6 : pp. 764–786
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Transport equation Interface Diffusion limit Asymptotic preserving Uniform numerical convergence X Y-geometry.
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