Volume 28, Issue 3
Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation

Shuang Tan, Wenjun Sun, Kun Xu, Junxia Wei & Guoxi Ni

Commun. Comput. Phys., 28 (2020), pp. 1189-1218.

Published online: 2020-07

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  • Abstract

In this paper, a time implicit unified gas kinetic scheme (IUGKS) for 3D multi-group neutron transport equation with delayed neutron is developed. The explicit scheme, implicit 1st-order backward Euler scheme, and 2nd-order Crank-Nicholson scheme, become the subsets of the current IUGKS. In neutron transport, the microscopic angular flux and the macroscopic scalar flux are fully coupled in an implicit way with the combination of dual-time step technique for the convergence acceleration of unsteady evolution. In IUGKS, the computational time step is no longer limited by the Courant-Friedrichs-Lewy (CFL) condition, which improves the computational efficiency in both steady and unsteady simulations with a large time step. Mathematically, the current scheme has the asymptotic preserving (AP) property in recovering automatically the diffusion solution in the continuum regime. Since the explicit scanning along neutron traveling direction within the computational domain is not needed in IUGKS, the scheme can be easily extended to multi-dimensional and parallel computations. The numerical tests demonstrate that the IUGKS has high computational efficiency, high accuracy, and strong robustness when compared with other schemes, such as the explicit UGKS, the commonly used finite difference, and finite volume methods. This study shows that the IUGKS can be used faithfully to study neutron transport in practical engineering applications.

  • Keywords

UGKS, neutron transport, time implicit scheme.

  • AMS Subject Headings

82D75, 82C70, 82C40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1189, author = {Shuang Tan , and Wenjun Sun , and Kun Xu , and Junxia Wei , and Guoxi Ni , }, title = {Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {3}, pages = {1189--1218}, abstract = {

In this paper, a time implicit unified gas kinetic scheme (IUGKS) for 3D multi-group neutron transport equation with delayed neutron is developed. The explicit scheme, implicit 1st-order backward Euler scheme, and 2nd-order Crank-Nicholson scheme, become the subsets of the current IUGKS. In neutron transport, the microscopic angular flux and the macroscopic scalar flux are fully coupled in an implicit way with the combination of dual-time step technique for the convergence acceleration of unsteady evolution. In IUGKS, the computational time step is no longer limited by the Courant-Friedrichs-Lewy (CFL) condition, which improves the computational efficiency in both steady and unsteady simulations with a large time step. Mathematically, the current scheme has the asymptotic preserving (AP) property in recovering automatically the diffusion solution in the continuum regime. Since the explicit scanning along neutron traveling direction within the computational domain is not needed in IUGKS, the scheme can be easily extended to multi-dimensional and parallel computations. The numerical tests demonstrate that the IUGKS has high computational efficiency, high accuracy, and strong robustness when compared with other schemes, such as the explicit UGKS, the commonly used finite difference, and finite volume methods. This study shows that the IUGKS can be used faithfully to study neutron transport in practical engineering applications.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0050}, url = {http://global-sci.org/intro/article_detail/cicp/17691.html} }
TY - JOUR T1 - Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation AU - Shuang Tan , AU - Wenjun Sun , AU - Kun Xu , AU - Junxia Wei , AU - Guoxi Ni , JO - Communications in Computational Physics VL - 3 SP - 1189 EP - 1218 PY - 2020 DA - 2020/07 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2019-0050 UR - https://global-sci.org/intro/article_detail/cicp/17691.html KW - UGKS, neutron transport, time implicit scheme. AB -

In this paper, a time implicit unified gas kinetic scheme (IUGKS) for 3D multi-group neutron transport equation with delayed neutron is developed. The explicit scheme, implicit 1st-order backward Euler scheme, and 2nd-order Crank-Nicholson scheme, become the subsets of the current IUGKS. In neutron transport, the microscopic angular flux and the macroscopic scalar flux are fully coupled in an implicit way with the combination of dual-time step technique for the convergence acceleration of unsteady evolution. In IUGKS, the computational time step is no longer limited by the Courant-Friedrichs-Lewy (CFL) condition, which improves the computational efficiency in both steady and unsteady simulations with a large time step. Mathematically, the current scheme has the asymptotic preserving (AP) property in recovering automatically the diffusion solution in the continuum regime. Since the explicit scanning along neutron traveling direction within the computational domain is not needed in IUGKS, the scheme can be easily extended to multi-dimensional and parallel computations. The numerical tests demonstrate that the IUGKS has high computational efficiency, high accuracy, and strong robustness when compared with other schemes, such as the explicit UGKS, the commonly used finite difference, and finite volume methods. This study shows that the IUGKS can be used faithfully to study neutron transport in practical engineering applications.

Shuang Tan, Wenjun Sun, Kun Xu, Junxia Wei & Guoxi Ni. (2020). Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation. Communications in Computational Physics. 28 (3). 1189-1218. doi:10.4208/cicp.OA-2019-0050
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