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Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics

Publication ,  Journal Article
Li, Q; Lu, J; Sun, W
Published in: Journal of Computational Physics
July 1, 2015

In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the half-space solver in [20] to resolve the boundary layer equation and obtain the boundary data for the diffusion equation. The algorithms are validated by numerical experiments and also by error analysis for the pure diffusive scaling case.

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Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

July 1, 2015

Volume

292

Start / End Page

141 / 167

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

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Li, Q., Lu, J., & Sun, W. (2015). Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics. Journal of Computational Physics, 292, 141–167. https://doi.org/10.1016/j.jcp.2015.03.014
Li, Q., J. Lu, and W. Sun. “Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics.” Journal of Computational Physics 292 (July 1, 2015): 141–67. https://doi.org/10.1016/j.jcp.2015.03.014.
Li Q, Lu J, Sun W. Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics. Journal of Computational Physics. 2015 Jul 1;292:141–67.
Li, Q., et al. “Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics.” Journal of Computational Physics, vol. 292, July 2015, pp. 141–67. Scopus, doi:10.1016/j.jcp.2015.03.014.
Li Q, Lu J, Sun W. Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics. Journal of Computational Physics. 2015 Jul 1;292:141–167.
Journal cover image

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

July 1, 2015

Volume

292

Start / End Page

141 / 167

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences