CMFD加速在特征线法输运计算中的应用

为解决特征线法求解复杂几何条件下中子输运问题收敛速度慢的问题,将粗网扩散计算中的粗网有限差分(CMFD:Coarse-Mesh Finite Difference)加速方法运用于中子输运计算中.采用粗网有限差分加速方法对C5G7 MOX基准问题以及自定义的69群检验算例的计算表明,CMFD加速是一种十分高效的方法,可显著地提高特征线法求解中子输运问题的收敛速度,且问题规模越大,加速效果越明显.     

P1各向异性散射特征线方法研究及应用

基于各向同性散射的中子输运方程特征线方法,计算实际组件能谱时经输运修正后,散射矩阵中P0自散射截面可能出现一定量的负值,影响数值稳定性。本文开发了P1各向异性散射特征线方法,并研制了计算程序PEACH-A。压水堆栅元基准问题的验证结果表明,PEACH-A程序具有较高的计算精度。对典型富集度的UO_2、MOX燃料栅元及其组合问题进行了敏感性分析,结果表明,针对MOX燃料及富集度差异较大的UO_2燃料栅元组合问题有必要采用P1各向异性散射。     

线性源近似的中子输运方程特征线解法

基于非结构网格的中子输运方程特征线解法已成为堆芯设计程序中组件输运计算的标准方法之一。但现有的大部分特征线法程序均是基于平源近似的步特征线法模型开发的,平源近似是特征线法中除角度变量直接离散外又一基本假定。本工作提出一种基于线性源近似的中子输运方程特征线解法,并提出相关负中子源分布的修正方法。采用自行研制的数值计算软件PEACH,对OECD/NEAC5G7-MOX2D基准问题和自定义沸水堆小堆芯问题进行检验。数值计算结果表明,本工作提出的线性源近似特征线法模型在相同计算精度的前提下,占用更少的系统内存和运行时间。     

基于组件模块化特征线方法的中子输运计算研究

栅元模块化特征线方法(MOC)在处理压水堆组件水隙等问题上存在几何处理上的困难。为了克服这些问题,采用Fortran语言开发了基于组件模块化特征线方法(AMRT)的中子输运计算程序NECP-Medlar,并采用两重粗网有限差分方法进行加速。2D C5G7基准题和典型压水堆组件问题的数值计算结果表明,该程序具有良好的计算精度和较高的计算效率,并且能够通过直接计算组件之间的水隙,较精确地描述组件中子通量密度的分布。     

基于模块化射线追踪的矩阵MOC方法(2)——数值验证

根据对模块化矩阵特征线(MOC)方法进行的理论研究结果,采用C++语言编制模块化矩阵MOC程序。为验证该程序的计算精度和计算效率,对沸水堆(BWR)栅格、UO2组件、2D C5G7三个基准题进行计算。数值结果表明,模块化矩阵MOC方法具有良好的计算精度和较高的计算效率。     

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。     

特征线几何预处理方法比较

网格划分、特征线间距、角度求积组、极角数目和方位角大小等几何预处理过程对特征线法的计算精度和计算效率有较大影响。基于步特征线法开发输运程序,通过数值计算验证所开发程序的正确性并分析两种特征线扫描方法(首尾相间循环扫描法、首尾相接循环扫描法)以及网格划分、特征线间距、角度求积组、极角数目、方位角大小对计算精度的影响。结果表明,开发的程序准确可靠;首尾相间循环扫描方法的收敛速度比首尾相接循环扫描方法慢。     

一维特征线法中子输运程序开发及验证

为探讨两维/一维综合法堆芯分析方法,本文基于特征线法研制了一维中子输运程序--PEACH-1D.不同于通常的平源近似特征线方法,PEACH-1D可对子区的中子源项作线性近似;程序运用指数函数插值表和渐近源外推技术来加速计算过程.相关数值结果表明,PEACH-1D具有很高的计算精度和效率,线性源近似的特征线法具备处理较粗网格的能力,值得推广.     

三维特征线方法中的线性源近似

提出了一种在网格内部采用线性源分布的特征线方法,并且编写了线性源特征线方法程序TCM_L.数值计算结果表明,线性源特征线方法的计算精度高于平源特征线方法和简化线性特征线格式SLC;使用大网格计算的线性源特征线方法在保证计算精度的同时可以节省大量的存储空间和计算时间.     

提高子群法共振自屏计算精度研究

基于自行研制的子群法与特征线法相结合的中子共振自屏计算程序SGMOC,研究提高子群法计算精度的2种方法.数值验证表明,2种方法都能提高共振自屏计算精度.其中,采用随机干涉近似求解条件概率的共振干涉效应处理的修正效果约为(0.02％～0.23％)△k/k;考虑共振散射的修正效果约为0.1％△k/k;综合运用2种方法的修正效果约为(0.03％ ～0.27％)△k/k.     

Reduction in spatial discretization error in the method of characteristics by using the mobile-chord ray tracing method

The mobile-chord method is applied to the method of characteristics (MOC) to reduce the spatial discretization error in ray traces. In the mobile-chord method, the offset of a ray trace in a strip depends on the azimuthal angle and this variation cancels the spatial discretization error of each ray trace. Although the mobile-chord method has been employed in the evaluation of the collision probability, it has not yet been applied to the MOC. The mobile-chord method is implemented in the AEGIS code, which is a lattice physics code based on the MOC. Verification calculations are carried out for the pin-cell and whole core geometries of the C5G7 benchmark problem by using UO₂ and mixed oxide (MOX) fuels. The calculation results indicate that the spatial discretization error in the mobile-chord method is smaller than that in the equidistant ray tracing method, which is commonly used in conventional MOC codes. Since the mobile-chord method can be used along with the cyclic ray tracing method, it is expected to be an attractive candidate for conventional MOC codes.     

基于OpenMP的中子输运方程特征线法并行计算研究

特征线法是目前求解反应堆中子输运方程的主要计算方法之一。本文开发了基于OpenMP的中子输运方程特征线法并行计算程序,以提高特征线法的计算效率。OpenMP是共享存储体系结构上的一个并行编程模型,采用Fork-Join并行执行方式,适合于SMP共享内存多处理系统和多核处理器体系结构。通过相关基准题测试验证,表明所开发的程序在有效增殖因数以及相对中子通量(归一化栅元功率)分布等参数上都能取得良好的精度,且使用OpenMP能取得良好的加速效果,使计算时间显著减少。     

数字化反应堆高保真中子学程序SHARK研发

SHARK程序是由中国核动力研究设计院新近研发的基于全堆芯确定论非均匀输运理论体系的数字化反应堆软件。该软件从多群数据库的截面与共振数据出发,采用改进子群方法刻画有效共振截面的复杂非均匀效应,采用二维/一维或准三维特征线方法开展堆芯层面非均匀输运计算。目前该程序的定态微观问题计算能力已建立完毕。数值结果显示,SHARK程序对于商用压水堆相关基准问题具有良好的计算精度和效率。     

一种通过边界注量率耦合的MOC和SN二维耦合中子输运方法

当使用特征线方法（MOC）计算堆外探测器或某些特殊的重水慢化轻水冷却的实验堆时,因其活性区外部结构材料或慢化剂区域过大,密集的特征线会导致计算资源大量浪费。为解决这一问题,提出了一种新的基于MOC和离散纵标（S_N）节块法的耦合输运方法,并在数值反应堆物理计算程序NECP-X中实现。该方法将计算区域划分为MOC域（包括活性区等复杂结构区域）和S_N域（包括慢化剂和反射层等简单结构区域）,然后对2个区域的网格进行混合扫描,通过区域交界面的角注量率进行耦合;同时提出了一些可行的方法来减缓耦合边界角注量率带来的误差。最后通过二维C5G7基准题和全堆芯问题的测试来验证耦合方法的计算效果,数值结果表明该方法具有良好的计算效率和精度。      

Reduction of MOC discretization errors through a minimization of source ratio variances

A new technique to reduce discretization errors for ray tracing in the method of characteristics (MOC) is proposed focusing on depletion calculations of single and multi-assembly geometries. In order to efficiently carry out depletion calculations, a calculation scheme using the superhomogenization (SPH) method can be used. However, the discretization errors are caused by changes of neutron sources and total cross sections according to a depletion. This fact means that improvement of accuracy cannot be expected by the calculation scheme with the SPH method when changes of the above parameters are significant. In order to mitigate this problem, a new approach is developed. In the new approach, the discretization errors are reduced by minimizing a variance of a certain parameter which is composed of a ratio of neutron source to total cross section. The verification results suggest that accuracy is degraded by the SPH method as expected especially in a geometry where neutron sources and total cross sections are drastically changing through a depletion. On the other hand, the new approach gives more accurate results compared to the conventional MOC in all calculation cases. Consequently, improvement of calculation efficiency by the new approach is confirmed.     

An acceleration technique for 2D MOC based on Krylov subspace and domain decomposition methods

The method of characteristics (MOC) has great geometrical flexibility but poor computational efficiency in neutron transport calculations. The generalized minimal residual (GMRES) method, a type of Krylov subspace method, is utilized to accelerate a 2D generalized geometry characteristics solver AutoMOC. In this technique, a form of linear algebraic equation system for angular flux moments and boundary fluxes is derived to replace the conventional characteristics sweep (i.e. inner iteration) scheme, and then the GMRES method is implemented as an efficient linear system solver. This acceleration method is proved to be reliable in theory and simple for implementation. Furthermore, as introducing no restriction in geometry treatment, it is suitable for acceleration of an arbitrary geometry MOC solver. However, it is observed that the speedup decreases when the matrix becomes larger. The spatial domain decomposition method and multiprocessing parallel technology are then employed to overcome the problem. The calculation domain is partitioned into several sub-domains. For each of them, a smaller matrix is established and solved by GMRES; and the adjacent sub-domains are coupled by “inner-edges”, where the trajectory mismatches are considered adequately. Moreover, a matched ray tracing system is developed on the basis of AutoCAD, which allows a user to define the sub-domains on demand conveniently. Numerical results demonstrate that the acceleration techniques are efficient without loss of accuracy, even in the case of large-scale and strong scattering problems in complex geometries.     

Convergence analysis of MOC inner iterations with large negative self-scattering cross-section

When the transport correction is applied to the total cross-section, the self-scattering cross-section could have a negative value in order to preserve the balance of partial cross-sections. The negative self-scattering cross-section may lead to a negative impact on the convergence behavior for the method of characteristics (MOC), especially in a problem with large moderator regions containing hydrogen. In order to address this issue, the spectral radius of the inner iteration of MOC is theoretically estimated for various self-scattering cross-sections. It is found that the spectral radius of the inner iteration of MOC could exceed unity for a large negative self-scattering cross-section, which results in numerical divergence. A countermeasure for the divergence using the successive over relaxation method is also discussed in this paper.     

Development and verification of an MOC code employing assembly modular ray tracing and efficient acceleration techniques

In this paper, we report the development and verification of a method of characteristics (MOC) code, PEACH, at Shanghai Jiao Tong University. Both the usual flat-source step characteristics (SC) scheme and the linear source (LS) approximation scheme are adopted for the tracking calculation along the neutron trajectory. The assembly-based modular ray tracing (AMRT) technique that possesses a good geometric flexibility and high efficiency is employed, which makes PEACH able to deal with practical LWR assembly and core problems. Moreover, in order to reduce the computational time of the MOC iteration process, both the multi/few-group two-level cell-based coarse mesh finite difference (CMFD) acceleration and the exponential function interpolation technique are used. This results in a significant acceleration. Numerical results for the OECD NEA C5G7 MOX benchmark problem and a 69-group BWR mini-core problem demonstrate that PEACH is accurate and efficient. Numerical results also demonstrate that the LS scheme is more efficient than the SC scheme, taking less time and system memory to generate results of comparable accuracy. In addition, we find that MOC with CMFD acceleration always converges with almost the same number of outer iterations regardless of the physical problem size and the discretization parameters used. This shows an ideal linear relationship between the run time and the geometric size of the problem.