TY - GEN
T1 - A Unified Framework of Stabilized Finite Element Method for Solving the Boltzmann Transport Equation
AU - Cao, Liangzhi
AU - Fang, Chao
AU - Li, Yifei
AU - He, Qingming
N1 - Publisher Copyright:
© 2022 Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022. All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modify the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embed it in the Galerkin weak form yields a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods are similar with the same stabilization parameter, and all these stabilized techniques can obtain correct and stable solution.
AB - This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modify the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embed it in the Galerkin weak form yields a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods are similar with the same stabilization parameter, and all these stabilized techniques can obtain correct and stable solution.
KW - Approximate residual equation
KW - Boltzmann transport equation
KW - Stabilization parameter
KW - Stabilized finite element methods
UR - https://www.scopus.com/pages/publications/85184961949
U2 - 10.13182/PHYSOR22-37439
DO - 10.13182/PHYSOR22-37439
M3 - 会议稿件
AN - SCOPUS:85184961949
T3 - Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022
SP - 1983
EP - 1995
BT - Proceedings of the International Conference on Physics of Reactors, PHYSOR 2022
PB - American Nuclear Society
T2 - 2022 International Conference on Physics of Reactors, PHYSOR 2022
Y2 - 15 May 2022 through 20 May 2022
ER -