求解中子输运方程的保正及S_(2)综合加速方法  

The Combination of S_(2)Preconditioning and Positivity-preserving Schemes for Solving the Neutron Transport Equation

作　　者：薛雅惠 袁达明 XUE Yahui;YUAN Daming(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022;Jiangxi Provincial Center for Applied Mathematics,Nanchang 330022)

机构地区：[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

出　　处：《工程数学学报》2024年第5期980-990,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(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。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.

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 

分 类 号：O24[理学—计算数学]