在线咨询
中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (5): 980-990.doi: 10.3969/j.issn.1005-3085.2024.05.014

• • 上一篇    

求解中子输运方程的保正及$S_2$综合加速方法

薛雅惠1,   袁达明1,2   

  1. 1. 江西师范大学数学与统计学院，南昌  330022
    2. 江西省应用数学中心，南昌  330022
  • 收稿日期:2023-01-18 接受日期:2023-12-15 出版日期:2024-10-15
  • 通讯作者: 袁达明 E-mail: dmyuan@jxnu.edu.cn
  • 基金资助:
    国家自然科学基金 (11861039).

The Combination of $S_2$ Preconditioning and Positivity-preserving Schemes for Solving the Neutron Transport Equation

XUE Yahui1,   YUAN Daming1,2   

  1. 1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022
    2. Jiangxi Provincial Center for Applied Mathematics, Nanchang 330022
  • Received:2023-01-18 Accepted:2023-12-15 Online:2024-10-15
  • Contact: D. Yuan. E-mail address: dmyuan@jxnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11861039).

摘要：

中子输运方程的数值方法中，保正性和迭代收敛速度都是重要且具有挑战性的问题。对于一维板几何中子输运方程，采用$S_2$综合加速度法和保正方法相结合的算法进行求解。对于中子输运方程和$S_2$方程，采用线性间断Galerkin方法对其离散，并使用两种限制器得到非负解，这些限制器是易于实现的。将算法用于求解Reed问题，得到的数值结果验证了方法的有效性。

关键词: 中子输运方程, 保正算法, $S_2$综合加速度, 线性间断Galerkin方法

Abstract:

Both positivity-preserving and iteration acceleration techniques are key issues when employing numerical methods to solve neutron transport equation. An algorithm combining $S_2$ synthetic acceleration method and positivity-preserving techniques to solve neutron transport equation that defined in one-dimensional planar geometry. The linear discontinuous Galerkin methods are applied to solve both the transport equation and $S_2$ equations. Two kind of simple limiters are involved. The numerical results for solving the classical Reed problem testify the efficiency of our methods.

Key words: neutron transport equation, positivity-preserving, $S_2$ synthetic acceleration, linear discontinuous Galerkin method

中图分类号: