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

Yahui Wang, Ming Xie & Yu Ma

DOI: 10.4208/cicp.OA-2017-0203

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 = {Yahui Wang, Ming Xie and Yu Ma}, 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 AU - Yahui Wang, Ming Xie & Yu Ma 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 and Yu Ma. (2019). 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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