Volume 25, Issue 5
Neutron Discrete Velocity Boltzmann Equation and Its Finite Volume Lattice Boltzmann Scheme

Yahui Wang, Ming Xie & Yu Ma

Commun. Comput. Phys., 25 (2019), pp. 1446-1468.

Published online: 2019-01

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  • Abstract

Simulation of neutron transport process plays an important role in nuclear reactor computation and the numerical technique becomes the focus of nuclear reactor engineering. This paper provides a neutron finite volume lattice Boltzmann method (NFV-LBM) for solving the neutron discrete velocity Boltzmann equation (NDVBE), in which the NDVBE is deduced from the neutron transport equation (NTE) and the NFV-LBM is obtained by integrating the NDVBE. The macroscopic conservation equations recovered from the NDVBE via multi-scale expansion shows that the NDVBE has higher-order accuracy than diffusion theory, and the numerical solutions of neutron transport problems reveal the flexibility and applicability of NFV-LBM. This paper may provide some alternative perspectives for solving the NTE and some new ideas for researching the relationship between the NTE and other approximations.

  • Keywords

Neutron transport, neutron discrete velocity Boltzmann equation, neutron finite volume lattice Boltzmann, diffusion theory.

  • AMS Subject Headings

60-08, 60J60, 62E17, 65C20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-1446, author = {}, title = {Neutron Discrete Velocity Boltzmann Equation and Its Finite Volume Lattice Boltzmann Scheme}, journal = {Communications in Computational Physics}, year = {2019}, volume = {25}, number = {5}, pages = {1446--1468}, abstract = {

Simulation of neutron transport process plays an important role in nuclear reactor computation and the numerical technique becomes the focus of nuclear reactor engineering. This paper provides a neutron finite volume lattice Boltzmann method (NFV-LBM) for solving the neutron discrete velocity Boltzmann equation (NDVBE), in which the NDVBE is deduced from the neutron transport equation (NTE) and the NFV-LBM is obtained by integrating the NDVBE. The macroscopic conservation equations recovered from the NDVBE via multi-scale expansion shows that the NDVBE has higher-order accuracy than diffusion theory, and the numerical solutions of neutron transport problems reveal the flexibility and applicability of NFV-LBM. This paper may provide some alternative perspectives for solving the NTE and some new ideas for researching the relationship between the NTE and other approximations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0203}, url = {http://global-sci.org/intro/article_detail/cicp/12957.html} }
TY - JOUR T1 - Neutron Discrete Velocity Boltzmann Equation and Its Finite Volume Lattice Boltzmann Scheme JO - Communications in Computational Physics VL - 5 SP - 1446 EP - 1468 PY - 2019 DA - 2019/01 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0203 UR - https://global-sci.org/intro/article_detail/cicp/12957.html KW - Neutron transport, neutron discrete velocity Boltzmann equation, neutron finite volume lattice Boltzmann, diffusion theory. AB -

Simulation of neutron transport process plays an important role in nuclear reactor computation and the numerical technique becomes the focus of nuclear reactor engineering. This paper provides a neutron finite volume lattice Boltzmann method (NFV-LBM) for solving the neutron discrete velocity Boltzmann equation (NDVBE), in which the NDVBE is deduced from the neutron transport equation (NTE) and the NFV-LBM is obtained by integrating the NDVBE. The macroscopic conservation equations recovered from the NDVBE via multi-scale expansion shows that the NDVBE has higher-order accuracy than diffusion theory, and the numerical solutions of neutron transport problems reveal the flexibility and applicability of NFV-LBM. This paper may provide some alternative perspectives for solving the NTE and some new ideas for researching the relationship between the NTE and other approximations.

Yahui Wang, Ming Xie & Yu Ma. (2020). Neutron Discrete Velocity Boltzmann Equation and Its Finite Volume Lattice Boltzmann Scheme. Communications in Computational Physics. 25 (5). 1446-1468. doi:10.4208/cicp.OA-2017-0203
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