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求解中子输运方程的保正及S2综合加速方法

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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S2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S2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.
The Combination of S2 Preconditioning and Positivity-preserving Schemes for Solving the Neutron Transport Equation
Both positivity-preserving and iteration acceleration techniques are key issues when employing numerical methods to solve neutron transport equation.An algorithm combining S2 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 S2 equations.Two kind of simple limiters are involved.The numerical results for solving the classical Reed problem testify the efficiency of our methods.

neutron transport equationpositivity-preservingS2 synthetic accelerationlinear discontinuous Galerkin method

薛雅惠、袁达明

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江西师范大学数学与统计学院,南昌 330022

江西省应用数学中心,南昌 330022

中子输运方程 保正算法 S2综合加速度 线性间断Galerkin方法

国家自然科学基金

11861039

2024

工程数学学报
西安交通大学

工程数学学报

CSTPCD北大核心
影响因子:0.302
ISSN:1005-3085
年,卷(期):2024.41(5)