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A discrete-ordinates variational nodal method for heterogeneous neutron Boltzmann transport problems
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2024-07-16 , DOI: 10.1016/j.camwa.2024.06.032 Qizheng Sun , Xiaojing Liu , Xiang Chai , Hui He , Tengfei Zhang
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2024-07-16 , DOI: 10.1016/j.camwa.2024.06.032 Qizheng Sun , Xiaojing Liu , Xiang Chai , Hui He , Tengfei Zhang
This study introduces an unstructured variational nodal method (UVNM-S), also recognized as the hybridized discontinuous Galerkin (HDG) method, for solving heterogeneous neutron Boltzmann transport problems. The UVNM-S solves the variational formulation of neutron Boltzmann transport equation (NBTE) by meshing the problem domain with non-overlapping nodes, i.e. the meshes. Lagrange multipliers are introduced along nodal interfaces enforcing neutron conservation. The interface unknowns are globally coupled and solved as the Dirichlet data to recover local within-node unknowns. Unstructured meshes are handled using the coordinate transformation technique, while the angular variables are discretized using the discrete-ordinates (S) method. Furthermore, within the framework of the UVNM-S, the nonlinear diffusion acceleration (NDA) is incorporated to tackle the issue of slow convergence of the power iteration (PI). Besides, the volume correction method is developed to facilitate the implementation of the UVNM-S for heterogeneous problems. The 2D and 3D C5G7 benchmark problems and the SIMONS test problem are utilized to verify the suggested methods. According to numerical results, UVNM-S exhibits geometric compatibility and precision in a variety of applications. Moreover, the volume correction method yields a speed-up ratio of around 10, and the NDA method provides a 6-12 speed-up ratio.
中文翻译:
异质中子玻尔兹曼输运问题的离散坐标变分节点法
本研究引入了一种非结构化变分节点法(UVNM-S),也称为混合不连续伽辽金(HDG)法,用于解决异质中子玻尔兹曼输运问题。 UVNM-S 通过将问题域与非重叠节点(即网格)划分网格来求解中子玻尔兹曼输运方程(NBTE)的变分公式。沿着节点界面引入拉格朗日乘数以强制中子守恒。接口未知数被全局耦合并作为狄利克雷数据求解,以恢复局部节点内未知数。非结构化网格使用坐标变换技术进行处理,而角度变量则使用离散坐标 (S) 方法进行离散化。此外,在UVNM-S的框架内,引入了非线性扩散加速(NDA)来解决功率迭代(PI)收敛缓慢的问题。此外,还开发了体积校正方法,以方便 UVNM-S 针对异构问题的实现。利用2D和3D C5G7基准问题以及SIMONS测试问题来验证所提出的方法。根据数值结果,UVNM-S 在各种应用中表现出几何兼容性和精度。此外,体积校正方法产生约10的加速比,而NDA方法提供6-12的加速比。
更新日期:2024-07-16
中文翻译:
异质中子玻尔兹曼输运问题的离散坐标变分节点法
本研究引入了一种非结构化变分节点法(UVNM-S),也称为混合不连续伽辽金(HDG)法,用于解决异质中子玻尔兹曼输运问题。 UVNM-S 通过将问题域与非重叠节点(即网格)划分网格来求解中子玻尔兹曼输运方程(NBTE)的变分公式。沿着节点界面引入拉格朗日乘数以强制中子守恒。接口未知数被全局耦合并作为狄利克雷数据求解,以恢复局部节点内未知数。非结构化网格使用坐标变换技术进行处理,而角度变量则使用离散坐标 (S) 方法进行离散化。此外,在UVNM-S的框架内,引入了非线性扩散加速(NDA)来解决功率迭代(PI)收敛缓慢的问题。此外,还开发了体积校正方法,以方便 UVNM-S 针对异构问题的实现。利用2D和3D C5G7基准问题以及SIMONS测试问题来验证所提出的方法。根据数值结果,UVNM-S 在各种应用中表现出几何兼容性和精度。此外,体积校正方法产生约10的加速比,而NDA方法提供6-12的加速比。