[P37] Derivation of a multigroup diffusion equation for nonclassical problems

Conference paper

Lisa S. Enomoto, Hermes Alves Filho, Richard Vasques
Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Niagara Falls, Canada, 2023 Aug

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APA Click to copy
Enomoto, L. S., Filho, H. A., & Vasques, R. (2023). [P37] Derivation of a multigroup diffusion equation for nonclassical problems. In Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Niagara Falls, Canada.

Chicago/Turabian Click to copy
Enomoto, Lisa S., Hermes Alves Filho, and Richard Vasques. “[P37] Derivation of a Multigroup Diffusion Equation for Nonclassical Problems.” In Proceedings of International Conference on Mathematics &Amp; Computational Methods Applied to Nuclear Science &Amp; Engineering, Niagara Falls, Canada, 2023.

MLA Click to copy
Enomoto, Lisa S., et al. “[P37] Derivation of a Multigroup Diffusion Equation for Nonclassical Problems.” Proceedings of International Conference on Mathematics &Amp; Computational Methods Applied to Nuclear Science &Amp; Engineering, Niagara Falls, Canada, 2023.

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@inproceedings{lisa2023a,
  title = {[P37] Derivation of a multigroup diffusion equation for nonclassical problems},
  year = {2023},
  month = aug,
  journal = {Proceedings of International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Niagara Falls, Canada},
  author = {Enomoto, Lisa S. and Filho, Hermes Alves and Vasques, Richard},
  month_numeric = {8}
}

ABSTRACT: We have derived an asymptotic approximation to the nonclassical energy-dependent transport equation with isotropic scattering. This approximation reduces to the classical multigroup diffusion equation under the assumption of classical transport, and therefore it consists of a generalization of the classical theory. The nonclassical multigroup diffusion equation can be implemented in existing multigroup diffusion codes since it preserves the same form of the classical equation but with modified parameters. We present analytical solutions to the nonclassical multigroup diffusion equation for three test problems in an one-dimensional (1-D) spatially periodic diffusive system consisting of alternating solid and void layers randomly placed along the x-axis. To assess the accuracy of these solutions, we compare against benchmark results obtained by (i) generating a large number of physical realizations of the system, (ii) numerically solving the (classical) transport equation in each realization, and (iii) ensemble-averaging the solutions over all physical realizations. The solution of the nonclassical multigroup diffusion equation asymptotically converges to the benchmark numerical solutions as the system becomes more diffusive, validating the analysis presented.