R-Z几何中子输运方程的球谐函数方法

从二阶自共轭角注量率(SAAF: Self-Adjoint Angular Flux)中子输运方程出发,在二维圆柱坐标系下利用球谐函数对角度变量进行展开,推导出了一组关于空间变量的偏微分方程组,然后采用有限元方法进行了空间离散,编写了二维圆柱坐标系下的球谐函数输运计算程序.对一系列例题进行校验的数值结果表明,该方法具有较高的计算精度,克服了射线效应.     

深度学习方法求解中子输运方程的微分变阶理论

中子输运方程是核反应堆物理分析计算的基本方程，针对深度学习技术求解输运方程因定积分项带来的困难，本文提出了微分变阶理论：将输运方程定积分项变换为对应的原函数，其他部分的角通量密度项表示为原函数高阶微分形式，从而将具有微积分形式的输运方程转换为纯粹的高阶微分方程；给出了变换后的原函数定解约束条件，以及对应的边界条件形式；构造了由原函数方程、边界条件、原函数定解、特征值约束共同形成的加权损失函数，利用深度学习使得神经网络逼近原函数；通过将原函数求导进行微分降阶，最终得到原输运方程角通量密度的数值解。针对多个平板、球几何例题进行了数值验证，获得了具有连续性特点的计算结果，证明了本文理论及相关方法的正确性，从而为中子输运方程的数值求解方法探索新的技术途径。     

用于复杂环境下中子时空动力学计算的简化球谐函数方法

将简化球谐函数(SPN)方法用于离散输运时空动力学方程的角度变量,应用有限元方法离散其空间变量,用全隐式向后差分离散时间变量,用时间积分法求解缓发中子先驱核浓度方程,建立了复杂环境下输运时空动力学计算的理论模型.根据该模型编制了非结构网格多维输运时空动力学计算程序,数值计算结果表明,该方法可以应用于复杂环境下中子输运时空动力学计算.     

定态中子输运方程本征值计算方法研究

散射源项各向异性展开阶数较大或者离散纵标方法的角度离散方向较多时,中子输运方程本征值的计算迭代容易失败。为了克服该问题,本文通过数学上的推导,构造了中子输运方程α本征值迭代求解的一种新方法,数值算例表明该方法提高了收敛速度,不收敛的问题也得到明显改善。对keff本征值的计算进行改进,改进后的方法不依赖迭代初值,数值算例表明改进方法的计算结果较好。     

球谐函数有限元程序NECP-FISH的开发及其在聚变堆包层中子学分析中的应用

球谐函数有限元方法采用非结构网格求解中子输运方程,具备处理复杂几何的能力;同时又可避免离散纵标方法所造成的射线效应。本文从一阶中子输运方程出发,通过方程的弱形式推导了球谐函数多尺度有限元方法,并基于此方法开发了中子学分析程序NECP-FISH。通过在前后处理平台SALOME中开发接口程序,实现了程序的建模可视化和计算结果可视化。应用此程序计算了氦冷陶瓷包层,数值结果表明NECP-FISH对中子通量密度、氚增殖比和中子释热的计算结果与蒙特卡罗程序NECP-MCX吻合良好。氚增殖比相对偏差为0.56%,所有区域的中子释热偏差均在6%以内。     

中子输运计算界面流方法的数学共扼方程

以子区内中子源为常源近似条件下的中子积分输运方程为前向方程,推导了中子积分输运方程界面流算法在六角形几何情况下的数学共扼方程;介绍了该数学共扼方程求解的内、外迭代策略,并对前向方程计算程序TPHEX进行了改造,得到了常源近似情况下数学共扼方程计算程序TFHEX_J0。通过算例校验表明TPHEX_J0与TPHEX程序所计算的系统本征值符合良好,TFHEX_J0程序的计算结果是可靠的。     

非结构几何下二阶自共轭中子输运方程中的简化球谐函数方法研究

针对球谐函数方法求解中子输运方程时计算量大的缺点,将简化球谐函数(SPN)方法用于离散二阶自共轭(SAAF)中子输运方程的角度变量,同时应用有限元方法在非结构几何下进行空间离散,研究了简化球谐函数方法在SAAF方程中的应用.数值计算结果表明,SPN方法在保证计算精度的条件下,具有比PN方法快的计算速度,而且对于维数越高、网格数越多、展开阶数越高的问题,节省时间的效果越好.     

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。     

研究多群扩散理论的变分方法

本文将变分方法用于研究中子迁移问题,导出了严格渐近输运解所满足的、多群形式的扩散方程。该方程具有不同于P_1近似的扩散系数D_g,外推长度λ_g和连续性条件。扩散系数和外推距离是宏观输运截面∑_?~(tr),中子与核每次碰撞所产生的次级中子数C_g的函数。数值计算的结果表明,该方程在描述各种类型核系统的中子学问题时,其精度高于P_1近似,而计算工作量与P_1近似相近。     

离散节块输运方法在二维柱坐标系中的应用

讨论粗网离散节块法在二维柱坐标系内中子输运方程数值求解中的应用.给出方法的数学模型,在节块内中子通量采用二次近似,表面泄漏采用常数近似.根据所提出的理论模型,编制了考虑各向异性散射的二维节块输运程序DNSN/2D,并对一系列检验和基准问题作了计算.计算结果表明,与传统S_N方法相比,它具有很高的计算效率,在很粗的节块分割下具有非常高的精度.     

球坐标系下中子输运方程泄漏项的简便推导

An ingenious method has been discussed to provide a brief way for the derivation of the streaming term expression in the spherical geometry coordinate system. Instead of finding the differential relationship between the dihedral angle and the neutron transport distance, finding the geometry relationship between the dihedral angle and other plane angles is much easier. And then the differential relationship (easy to be derived) between the other plane angles and the neutron transport distance can be used to derive the expression of the streaming term in the spherical geometry coordinate system indirectly but easily. This method makes the derivation process easy and intuitive, with clear physical picture.     

非结构网格中子输运方程的球谐函数解法研究

从新的二阶自共扼角通量密度(SAAF：Self-Adjoint Angular Flux)中子输运方程出发．利用球谐函数对角度变量进行展开,导出了一组关于空间变量的偏微分方程组,中子通量密度的各个分量相互耦合,应用一定的迭代策略进行迭代求解。针对每一个方程,应用有限元方法对非结构网格进行离散求解。据此编写了二维球谐函数方法输运计算程序,对一系列基准题进行校算的数值结果表明,该方法具有较高的计算精度,克服了射线效应,并能用于非结构网格。     

Spherical harmonics method for neutron transport equation based on unstructured-meshes

Based on a new second-order neutron transport equation, self-adjoint angular flux (SAAF) equation, the spherical harmonics (PN) method for neutron transport equation on unstructured-meshes is derived. The spherical harmonics function is used to expand the angular flux. A set of differential equations about the spatial variable, which are coupled with each other, can be obtained. They are solved iteratively by using the finite element method on unstructured-meshes. A two-dimension transport calculation program is coded according to the model. The numerical results of some benchmark problems demonstrate that this method can give high precision results and avoid the ray effect very well.     

Lattice Boltzmann method for simulation of time-dependent neutral particle transport

In this paper,a novel model is proposed to investigate the neutron transport in scattering and absorbing medium.This solution to the linear Boltzmann equation is expanded from the idea of lattice Boltzmann method (LBM) with the collision and streaming process.The theoretical derivation of lattice Boltzmann model for transient neutron transport problem is proposed for the first time.The fully implicit backward difference scheme is used to ensure the numerical stability,and relaxation time and equilibrium particle distribution function are obtained.To validate the new lattice Boltzmann model,the LBM formulation is tested for a homogenous media with different sources,and both transient and steady-state LBM results get a good agreement with the benchmark solutions.     

Lattice Boltzmann method for simulation of time-dependent neutral particle transport

In this paper,a novel model is proposed to investigate the neutron transport in scattering and absorbing medium.This solution to the linear Boltzmann equation is expanded from the idea of lattice Boltzmann method (LBM) with the collision and streaming process.The theoretical derivation of lattice Boltzmann model for transient neutron transport problem is proposed for the first time.The fully implicit backward difference scheme is used to ensure the numerical stability,and relaxation time and equilibrium particle distribution function are obtained.To validate the new lattice Boltzmann model,the LBM formulation is tested for a homogenous media with different sources,and both transient and steady-state LBM results get a good agreement with the benchmark solutions.     

Application of forward and adjoint Monte Carlo coupling technique to detector system designs

Forward and adjoint Monte Carlo coupling technique has been developed for analyzing neutron streaming in a system with large geometry. Particles (neutron and adjoint particle) are scored by surface type estimators such as the next event surface crossing estimators and the boundary crossing estimators. The detector response is calculated by folding the calculated neutron and adjoint angular fluxes. The reliability and efficiency for this method were studied by solving a sample problem of neutron streaming through narrow sodium pipe embedded in an iron shield. This method turned out to give a figure of merit several times better than the conventional method. The applicability of the method to detector system design has been demonstrated by calculating the signal to noise ratio for the fuel failure detector with delayed neutron detection method, which is located behind the reactor shield of concrete. This method gives an advantage in clarifying the spatial channels for neutron streaming.     

Identification and properties of the fundamental expansion functions for neutron transport in an infinite homogeneous medium

Starting from the basic expression for the neutron flux due to a point source in an infinite homogeneous scattering and absorbing medium, the first few fundamental expansion functions corresponding to successive collisions are identified, and their analytic properties are presented, in spherical and plane geometry. Various representations of the functions are obtained in the form of power series, an expansion in a series of exponential integrals, and other integrals. The adequacy of traditional asymptotic forms is considered.     

A least-squares finite-element Sn method for solving first-order neutron transport equation

A discrete ordinates finite-element method for solving the two-dimensional first-order neutron transport equation is derived using the least-squares variation. It avoids the singularity in void regions of the method derived from the second-order equation which contains the inversion of the cross-section. Different from using the standard Galerkin variation to the first-order equation, the least-squares variation results in a symmetric matrix, which can be solved easily and effectively. To eliminate the discontinuity of the angular flux on the vacuum boundary in the spherical harmonics method, the angle variable is discretized by the discrete ordinates method. A two-dimensional transport simulation code is developed and applied to some benchmark problems with unstructured geometry. The numerical results verified the validity of this method.     

New Efficient Albedo Monte Carlo Method for Neutron Streaming Analyses

An efficient albedo Monte Carlo method newly developed has been studied by analyzing two types of experiments on neutron streaming. The method is characterized by employing the energy-angle dependent doubly differential albedos for slab, which can be calculated in a short computer time with a one-dimensional transport theory, such as the Sn method and more efficient invariant imbedding method. This paper describes the features of the present albedo Monte Carlo method, including fundamental formulas. In the analyses of the neutron streaming experiments, the calculated results agreed with the measured data within a factor of 2 for a benchmark experiment at the YAYOI reactor and within a factor of 3 for an SNR sodium duct mock-up experiment.

It is concluded that the present albedo Monte Carlo method is practical and applicable to the reactor shielding analysis concerning radiation streaming.