特征线方法(Method of Characteristics,MOC)因其具备强大的几何处理能力,且在计算过程中亦能兼顾计算成本和计算精度,被广泛应用于高保真数值模拟计算中。常见的中子输运计算方法除MOC外,还包括碰撞概率法(Collision Probability metho...特征线方法(Method of Characteristics,MOC)因其具备强大的几何处理能力,且在计算过程中亦能兼顾计算成本和计算精度,被广泛应用于高保真数值模拟计算中。常见的中子输运计算方法除MOC外,还包括碰撞概率法(Collision Probability method,CP)和界面流法(Interface Current method,IC)等。本文从方法理论以及数值计算两方面将MOC、CP和IC进行比较分析,评估其在pin-by-pin计算中的能力。同时在MOC计算中,不同的参数选择会对计算成本和计算精度产生影响,因此有必要进行敏感性分析以寻求最佳参数。本文首先将三种计算方法从原理上进行比较分析,再基于2D C5G7-MOX基准题完成了数值计算及MOC参数敏感性初步分析。计算结果表明:MOC在计算精度、计算效率和内存开销上均优于CP和IC。MOC的计算耗时和内存开销分别为23.9 min和37.5 MB,与参考解的相对误差仅为6.04×10^(-4)。而CP和IC的计算耗时分别为MOC的56.7倍和15.6倍,内存开销分别为MOC的407.7倍和32.8倍。进一步通过参数敏感性分析发现:网格划分对计算内存开销以及计算时间的影响最大,而极角的选择对计算精度的影响最大,并且给出一组综合优化建议参数:网格划分6×6,极角为GAUS且数目为2,方位角个数为30。该组参数的计算耗时为45.4 min,内存开销为264.7 MB,相对误差为5.9×10^(-5),归一化后的栅元均方根误差为0.002 55。展开更多
This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent,pinresolved neutron transport equations.VITAS uses the stiffness confinement method(SCM)for temporal di...This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent,pinresolved neutron transport equations.VITAS uses the stiffness confinement method(SCM)for temporal discretization to transform the transient equation into the corresponding transient eigenvalue problem(TEVP).To solve the pin-resolved TEVP,VITAS uses a heterogeneous variational nodal method(VNM).The spatial flux is approximated at each Cartesian node using finite elements in the x-y plane and orthogonal polynomials along the z-axis.Angular discretization utilizes the even-parity integral approach at the nodes and spherical harmonic expansions at the interfaces.To further lower the computational cost,a predictor–corrector quasi-static SCM(PCQ-SCM)was developed.Within the VNM framework,computational models for the adjoint neutron flux and kinetic parameters are presented.The direct-SCM and PCQ-SCM were implemented in VITAS and verified using the two-dimensional(2D)and three-dimensional(3D)exercises on the OECD/NEA C5G7-TD benchmark.In the 2D and 3D problems,the discrepancy between the direct-SCM solver’s results and those reported by MPACT and PANDAS-MOC was under 0.97%and 1.57%,respectively.In addition,numerical studies comparing the PCQ-SCM solver to the direct-SCM solver demonstrated that the PCQ-SCM enabled substantially larger time steps,thereby reducing the computational cost 100-fold,without compromising numerical accuracy.展开更多
文摘特征线方法(Method of Characteristics,MOC)因其具备强大的几何处理能力,且在计算过程中亦能兼顾计算成本和计算精度,被广泛应用于高保真数值模拟计算中。常见的中子输运计算方法除MOC外,还包括碰撞概率法(Collision Probability method,CP)和界面流法(Interface Current method,IC)等。本文从方法理论以及数值计算两方面将MOC、CP和IC进行比较分析,评估其在pin-by-pin计算中的能力。同时在MOC计算中,不同的参数选择会对计算成本和计算精度产生影响,因此有必要进行敏感性分析以寻求最佳参数。本文首先将三种计算方法从原理上进行比较分析,再基于2D C5G7-MOX基准题完成了数值计算及MOC参数敏感性初步分析。计算结果表明:MOC在计算精度、计算效率和内存开销上均优于CP和IC。MOC的计算耗时和内存开销分别为23.9 min和37.5 MB,与参考解的相对误差仅为6.04×10^(-4)。而CP和IC的计算耗时分别为MOC的56.7倍和15.6倍,内存开销分别为MOC的407.7倍和32.8倍。进一步通过参数敏感性分析发现:网格划分对计算内存开销以及计算时间的影响最大,而极角的选择对计算精度的影响最大,并且给出一组综合优化建议参数:网格划分6×6,极角为GAUS且数目为2,方位角个数为30。该组参数的计算耗时为45.4 min,内存开销为264.7 MB,相对误差为5.9×10^(-5),归一化后的栅元均方根误差为0.002 55。
基金supported by the National Natural Science Foundation of China (Nos. 12175138, U20B2011)the Young Talent Project of the China National Nuclear Corporation
文摘This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent,pinresolved neutron transport equations.VITAS uses the stiffness confinement method(SCM)for temporal discretization to transform the transient equation into the corresponding transient eigenvalue problem(TEVP).To solve the pin-resolved TEVP,VITAS uses a heterogeneous variational nodal method(VNM).The spatial flux is approximated at each Cartesian node using finite elements in the x-y plane and orthogonal polynomials along the z-axis.Angular discretization utilizes the even-parity integral approach at the nodes and spherical harmonic expansions at the interfaces.To further lower the computational cost,a predictor–corrector quasi-static SCM(PCQ-SCM)was developed.Within the VNM framework,computational models for the adjoint neutron flux and kinetic parameters are presented.The direct-SCM and PCQ-SCM were implemented in VITAS and verified using the two-dimensional(2D)and three-dimensional(3D)exercises on the OECD/NEA C5G7-TD benchmark.In the 2D and 3D problems,the discrepancy between the direct-SCM solver’s results and those reported by MPACT and PANDAS-MOC was under 0.97%and 1.57%,respectively.In addition,numerical studies comparing the PCQ-SCM solver to the direct-SCM solver demonstrated that the PCQ-SCM enabled substantially larger time steps,thereby reducing the computational cost 100-fold,without compromising numerical accuracy.
