非结构网格中子输运方程角度相关再平衡加速算法

利用最小二乘有限元离散纵标方法,对一阶中子输运方程进行离散求解,给出了基于非结构网格的角度相关再平衡加速算法及其外推算法.基准问题的计算结果表明,求解问题的计算时间可减少到原来的34%～50%,对强散射问题也同样有效.     

强各向异性散射中子输运方程加速方法

采用修正的PN方程加速中子输运方程的SN数值求解过程.并将该加速方法应用到国际通用的ANISN程序中,对其进行了数值检验.数值计算结果表明,本文加速方法可以使迭代次数大量减少,特别是对于强各向异性散射问题具有明显的加速效果.     

中子输运计算的角度多重网格加速和L-W外推加速技术

把角度多重网格(ANMG)加速方法及Lyusternik-Wagner(L-W)外推加速技术应用于三维多群离散纵标三角形节块稳态中子输运数值计算程序(DNTR).一系列输运问题的数值结果表明:ANMG加速方法具有较好的加速效果,且对强各向异性散射和强散射比问题有很强的适应性.在ANMG加速方法的基础上增加L-W外推加速技术后,可以使整体加速效果更加显著.     

二维中子输运方程计算的角度多重网格加速方法及外推加速技术

为提高中子输运问题的计算时程效率,本文采用角度多重网格(ANMG)加速方法加速源迭代过程,并在此基础上给出了Lyusternik-Wagner外推加速技术,并应用到中子输运方程最小二乘有限元计算程序LESFES中.数值结果表明:无论对于各向同性散射问题还是强各向异性散射问题,ANMG加速方法具有良好的加速效果;而且在ANMG加速方法的基础上增加Lyusternik-Wagner外推加速技术后,可以使整体加速效果更加明显.     

高保真中子输运计算的多级加速理论及应用

为解决高保真中子输运计算耗时严重的问题,本文提出了多级加速理论。其中,针对迭代求解过程,采用迭代加速的思路,即通过等价的低分辨率系统加速以减少迭代次数;针对瞬态求解,采用时间步加速方法,通过建立多级预估校正系统,实现在大时间步长下开展准确的高保真中子输运计算。最终引入不同分辨率系统的概念,将时间步加速方法与迭代加速方法整合形成一套完整的多级加速理论,并将其应用到精细化中子物理计算程序HNET中。采用典型瞬态基准题验证HNET程序加速效果。数值结果表明：多级加速理论能够在保证高保真中子输运计算精度的同时,极大地提升计算效率。     

中子输运方程的Daubechies小波角度离散

近年来对新型反应堆中广泛应用的混合氧化物(MOX)燃料的研究表明,中子通量密度在该型燃料栅元中随角度的分布呈现出剧烈的震荡,传统的角度离散方法很难对其进行很好的逼近.本研究利用具有紧支、正交特点的Daubechies小波离散中子输运方程的角度变量,建立了中子输运方程小波基函数展开的理论模型.将小波展开与离散纵标方法相结合,解决了二维张量积小波展开引入的大规模通量矩耦合问题,降低了耦合规模,实现了二维高阶小波展开的数值求解.数值校验证明:中子输运方程小波分析方法可以高精度地模拟复杂中子通量密度随角度的分布.     

中子导管输运特性的数值计算方法

采用自行编写的数值方法计算程序NCMP(Numeric Calculation Method Program)对中子导管的输运性能进行了计算,并分别与文献以及俄罗斯核物理研究所Pusenkov教授提供的计算结果进行了对比,符合得很好.结果表明该数值计算软件能够精确地计算中子导管的输运特性.     

瞬态中子输运计算程序的研制

开发编制了基于输运理论的瞬态中子动力学程序DOT4-T.该程序是在二维稳态离散纵标程序DOT4.2基础上开发的,对瞬态中子输运方程中的时间变量直接应用无条件稳定的隐式离散格式.为验证该程序的正确性,对一些一维和二维瞬态基准问题进行了校核计算,其结果与基准题吻合良好.     

GPU加速MOC输运计算性能分析研究

特征线方法(MOC)在求解堆芯规模中子输运方程时面临计算时间长的问题,加速和并行算法是目前研究的热点。基于MOC在特征线和能群层面的并行特性,采用统一计算设备构架(CUDA)编程规范,实现了基于图形处理器(GPU)的并行二维MOC算法。测试了菱形差分和步特征线法分别在双精度、混合精度及单精度浮点运算下的计算精度、效率及GPU加速效果。采用性能分析工具对GPU程序性能进行了分析,识别了程序性能瓶颈。结果表明:菱形差分和步特征线法在不同浮点运算精度下均表现出良好的计算精度;相比于CPU单线程计算,GPU加速效果在双精度和单精度情况下分别达到35倍和100倍以上。     

KYCORE程序中子输运计算的改进

KYCORE程序是在中国核动力研究设计院开发的二维组件计算程序KYLIN-2基础上开发的三维堆芯数值计算程序,其中中子输运部分采用径向特征线方法(MOC)与轴向离散坐标法(SN)直接角通量耦合的方法实现高精度计算,并通过粗网有限差分方法(CMFD)加速实现快速收敛。KYCORE程序因为计算流程的简化,导致可能出现不收敛,因此在计算方法和网格划分上做了改进,提高了计算的稳定性和包容性。通过与C5G7扩展基准题和蒙特卡罗程序的计算对比,数值验证了KYCORE输运部分计算的稳定性与准确性。     

Solutions of Monoenergetic Time Dependent Neutron Transport Equation in Slab Geometry

Approximate solutions to the one-velocity time dependent neutron transport equation are derived by means of the eigenfunction expansion method of Case for a slab geometry. A finite set of discrete time eigenvalues is determined by a simple formula. This formula, which is derived for the case of large slab thickness, is found to be valid also for fairly thin slabs. Each time eigenvalue generates a pair of spatial modes. The expansion coefficients to these modes are examined by numerical evaluation for various slab thicknesses. Higher spatial modes are found to play an important role in the transient time evolution of neutrons.     

Application of Finite Element Method to Two-Dimensional Multi-Group Neutron Transport Equation in Cylindrical Geometry

The finite element method is applied to the spatial variables of multi-group neutron transport equation in the two-dimensional cylindrical (r, z) geometry. The equation is discretized using regular rectangular subregions in the (r, z) plane. The discontinuous method with bilinear or biquadratic Lagrange's interpolating polynomials as basis functions is incorporated into a computer code FEMRZ. Here, the angular fluxes are allowed to be discontinuous across the subregion boundaries.

Some numerical calculations have been performed and the results indicated that, in the case of biquadratic approximation, the solutions are sufficiently accurate and numerically stable even for coarse meshes. The results are also compared with those obtained by a diamond difference S _n code TWOTRAN-II. The merits of the discontinuous method are demonstrated through the numerical studies.     

Numerical Solutions of Discrete-Ordinate Neutron Transport Equations Equivalent to PL Approximation in X-Y Geometry

A numerical method for solving the steady-state one-velocity neutron transport equation in x-y geometry is presented. It is based on the concept of combining the spherical harmonics theory with the discrete-ordinate method. The validity of the method is illustrated by several numerical computations using the TWOTRAN-PLXY code, formulated by modifying the ordinary discrete-ordinate code TWOTRAN-(x, y).

Through numerical studies, it is shown that the present method is effective for obtaining solutions of high accuracy, as well as for eliminating the ray effects present in the ordinary discrete-ordinate method. As for the techniques for accelerating the convergence of the iterative solutions, it is proved that the Chebyshev device works well for the present method, while whole-system rebalancing is found to be less effective.