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。     

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.     

基于最小二乘的线性源特征线方法研究

特征线方法一般采用平源近似来求解,平源近似需要大量较小的网格才能获得精确的结果,从而会消耗较多内存,影响计算效率.相比平源近似,线性源可在网格较少的情况下得到较精确的数值结果.本文提出一种基于最小二乘的线性源特征线方法,并通过计算压水堆栅元及C5G7基准题等算例,对该方法进行了分析.数值结果表明,基于最小二乘的线性源特...     

基于最小二乘的线性源特征线方法研究

特征线方法一般采用平源近似来求解,平源近似需要大量较小的网格才能获得精确的结果,从而会消耗较多内存,影响计算效率。相比平源近似,线性源可在网格较少的情况下得到较精确的数值结果。本文提出一种基于最小二乘的线性源特征线方法,并通过计算压水堆栅元及C5G7基准题等算例,对该方法进行了分析。数值结果表明,基于最小二乘的线性源特征线方法能在网格较少的情况下提供稳定、精确的数值结果。     

基于模块化特征线方法的二维/一维耦合输运程序开发

随着各种新堆型的提出,全堆芯非均匀计算的需求也日益迫切。基于需求和可行性的考虑,提出了二维/一维(2D/1D)耦合方法求解三维(3D)非均匀问题,国际上已经开发出许多这样的程序。本文基于模块化特征线方法开发了2D/1D耦合程序—MOCHA_2D1D,2D耦合程序计算采用模块化特征线方法,1D耦合程序计算采用Sn差分方法。经过验证,程序计算精度符合反应堆物理计算要求。     

基于DRAGON程序的二维/一维耦合堆芯输运计算程序开发

DRAGON程序能够进行三维特征线法(MOC)计算,但需大量的计算时间与内存,虽在其中引入大量近似并应用多种加速算法,仍无法满足工程应用的需求。基于DRAGON程序中现有的二维MOC计算模块,开发二维MOC与一维节块展开法(NEM)耦合的堆芯输运计算程序DRAGON_HEU,在三维粗网有限差分(CMFD)加速算法的全局框架下通过轴向和径向泄漏项将二维全堆非均匀栅元MOC计算与轴向均匀栅元扩散计算耦合,实现三维堆芯Pin-by-Pin计算。运用C5G7-3D三维扩展基准题验证DRAGON_HEU,计算结果表明:DRAGON_HEU能够节约大量计算时间且具有很高的计算精度。     

线性子链法在排放源项计算中的应用

根据线性子链法原理和流出物排放源项计算模型的特点,本文建立了全面自动搜索核素链的方法,覆盖了所有核素涉及到的核素链,推导出了排放源项模型的解析表达式,将复杂的衰变链分解为数条线性链,对每一条核素链分别进行解析计算得到每个核素的核素浓度。将这一方法用于核电厂排放源项的活度计算,并将本方法求解结果与PWR-GALE的ORIGEN求解模块的结果比较,以及将最终排放源项的计算结果与国内某核电厂排放源项比较,对比表明,大部分核素浓度计算结果与ORIGEN一致,短寿命核素浓度的计算中由于ORIGEN采用长期平衡近似以及衰变链简化处理后所得结果偏于保守;本方法计算排放源项所得结果与国内某核电厂排放源项结果非常符合。本方法应用了全面自动搜索的线性子链法,自动搜索添加衰变链,并使用解析法依次对每条衰变链的每个核素进行计算,使得计算结果更加全面,结果更准确。     

压水堆核电站活化产物源项计算程序CPAP的开发

活化产物为压水堆核电站中主要辐射源,有必要对其建立分析手段。分析了压水堆核电站堆芯外材料中活化产物源项的产生途径,建立了压水堆核电站堆芯外材料中活化产物源项的计算模型,并分别基于矩阵指数法和切比雪夫有理近似法求解所建立的计算模型。开发了具有良好人机界面的计算程序CPAP,并采用典型材料活化例题与国外同类软件进行了对比测试。测试结果表明:CPAP程序对于测试算例的计算结果与国外同类软件的计算结果之间的偏差在工程可接受的范围内。CPAP程序具有人机界面友好以及求解器可选的优点,可广泛应用于压水堆核电站的设计、运行和退役阶段。     

模块化2D/1D耦合特征线法MMOC程序开发及验证

本文基于耦合求解的思想,轴向、径向均采用特征线法（MOC）,通过开展2D/1D耦合MOC理论模型、模块化几何预处理方法研究,开发了2D/1D耦合MOC 3D中子输运求解程序MMOC,并开展了1D/2D/3D C5G7基准题验证。k_eff的相对误差分别为0.082%、0.045%、0.032%,该程序准确有效,计算精度满足中子输运计算的要求。     

基于首次碰撞源方法的多维SN射线效应研究

通过半解析法求解由孤立点源产生的未碰撞中子源项,进而求出首次碰撞源分布,以将孤立的源分布到更广的范围中,从而减轻由离散纵标法计算产生的射线效应。编制了适应于三维离散纵标计算程序CTDOS的射线效应减轻程序REM3D,与Kobayashi三维基准题的结果进行比对,证明了射线效应减弱的正确性与本程序的可行性。     

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.     

Evaluation of Dancoff Factors in Complicated Geometry using the Method of Characteristics

A simple and efficient method to estimate the Dancoff factor in a complicated geometry, named “the Neutron current method,” is presented in this paper. In this method, Dancoff factors are evaluated from the flux values obtained by the method of characteristics (MOC). By setting appropriate neutron sources in the non-fuel regions of target geometry and then executing fixed source calculation by MOC, the neutron current method can evaluate Dancoff factors for complicated geometry. It was demonstrated that the neutron current method can easily be adopted for complicated geometries, such as a PWR fuel assembly or large-scale geometry that is difficult to handle by the traditional collision probability method. By utilizing the neutron current method instead of a traditional collision probability method, the calculation time of Dancoff factors in complicated large geometry is drastically reduced.     

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.     

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。     

Application of the multigrid amplitude function method for time-dependent MOC based on the linear source approximation

ABSTRACT

An efficient numerical scheme for time-dependent MOC calculations is proposed. In the present scheme, one of the most successful factorization method, the multigrid amplitude function (MAF) method, is employed to achieve faster computation with the minimum degradation for the temporal integration of the scalar flux. In addition, the MAF method is re-derived based on the linear source approximation, which is not applied for time-dependent MOC calculations in the past studies as far as the authors’ knowledge, to reduce the spatial discretization error with the coarser flux region separation. The accuracy and computational time of the present scheme are evaluated through the calculation of the TWIGL and the C5G7-TD 2D benchmark problems. The present calculation results show that the present scheme is 6.2 times faster than the conventional method while achieving the same accuracy in the C5G7-TD benchmark problem.     

NECP-X中基于改进泄漏项分割技术的二维/一维耦合输运方法

二维/一维耦合输运方法较好地平衡了效率与精度,因此被广泛应用于一步法全堆芯输运计算。二维/一维耦合输运方法中,由于泄漏项在方程右端,导致二维特征线法(MOC)计算时方程右端总源项在迭代过程中可能成为负值,造成迭代发散。本文针对二维/一维耦合输运计算中的负源项问题,提出了一种改进的泄漏项分割方法。新的泄漏项分割方法可在不造成计算精度损失和仅增加有限内存的条件下,显著提高二维/一维耦合输运方法的稳定性。通过强泄漏算例、C5G7基准题、VERA-3A基准题等进行测试,表明该方法对提高二维/一维耦合输运方法稳定性具有显著的效果。     

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。