An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems

The heterogeneous variational nodal method(HVNM)has emerged as a potential approach for solving high-fidelity neutron transport problems.However,achieving accurate results with HVNM in large-scale problems using high-fidelity models has been challenging due to the prohibitive computational costs.This paper presents an efficient parallel algorithm tailored for HVNM based on the Message Passing Interface standard.The algorithm evenly distributes the response matrix sets among processors during the matrix formation process,thus enabling independent construction without communication.Once the formation tasks are completed,a collective operation merges and shares the matrix sets among the processors.For the solution process,the problem domain is decomposed into subdomains assigned to specific processors,and the red-black Gauss-Seidel iteration is employed within each subdomain to solve the response matrix equation.Point-to-point communication is conducted between adjacent subdomains to exchange data along the boundaries.The accuracy and efficiency of the parallel algorithm are verified using the KAIST and JRR-3 test cases.Numerical results obtained with multiple processors agree well with those obtained from Monte Carlo calculations.The parallelization of HVNM results in eigenvalue errors of 31 pcm/-90 pcm and fission rate RMS errors of 1.22%/0.66%,respectively,for the 3D KAIST problem and the 3D JRR-3 problem.In addition,the parallel algorithm significantly reduces computation time,with an efficiency of 68.51% using 36 processors in the KAIST problem and 77.14% using 144 processors in the JRR-3 problem.

NUMERICAL SIMULATION OF SINGLE-GROUP, STEADY STATE AND ISOTROPIC NEUTRON TRANSPORT EQUATION IN DIFFUSIVE REGIMES

We present an algorithm for numerical solution of transport equation in diffusive regimes, in which the transport equation is nearly singular and its solution becomes a solution of a diffusion equation. This algorithm, which is based on the Least-squares FEM in combination with a scaling transformation, presents a good approximation of a diffusion operator in diffusive regimes and guarantees an accurate discrete solution. The numerical experiments in 2D and 3D case are given, and the numerical results show that this algorithm is correct and efficient.

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 un- structured-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.

Development and validation of the code COUPLE3.0 for the coupled analysis of neutron transport and burnup in ADS

The analysis of the fuel depletion behavior is critical for maintaining the safety of accelerator-driven subcritical systems(ADSs). The code COUPLE2.0 coupling 3-D neutron transport and point burnup calculation was developed by Tsinghua University. A Monte Carlo method is used for the neutron transport analysis, and the burnup calculation is based on a deterministic method. The code can be used for the analysis of targets coupled with a reactor in ADSs. In response to additional ADS analysis requirements at the Institute of Modern Physics at the Chinese Academy of Sciences, the COUPLE3.0 version was developed to include the new functions of(1) a module for the calculation of proton irradiation for the analysis of cumulative behavior using the residual radionuclide operating history,(2) a fixed-flux radiation module for hazard assessment and analysis of the burnable poison, and(3) a module for multi-kernel parallel calculation, which improves the radionuclide replacement for the burnup analysis to balance the precision level and computational efficiency of the program. This paper introduces thevalidation of the COUPLE3.0 code using a fast reactor benchmark and ADS benchmark calculations. Moreover,the proton irradiation module was verified by a comparison with the analytic method of calculating the210 Po accumulation results. The results demonstrate that COUPLE3.0 is suitable for the analysis of neutron transport and the burnup of nuclides for ADSs.

Preliminary study on CAD-based method of characteristics for neutron transport calculation

Our new method makes use of a CAD-based automatic modeling tool, MCAM, for geometry modeling and ray tracing of particle transport in method of characteristics （MOC）. It was found that it could considerably enhance the capability of MOC to deal with more complicated models for neutron transport calculation. In our study, the diamond-difference scheme was applied to MOC to reduce the spatial discretization errors of the fiat flux approximation. Based on MCAM and MOC, a new 2D MOC code was developed and integrated into the SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical results demonstrated the feasibility and effectiveness of the new method for neutron transport calculation in MOC.

ASYMPTOTIC EXPANSION AND ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR THE TIME-DEPENDENT NEUTRON TRANSPORT PROBLEM IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

In this paper,the time-dependent neutron transport integro-differential equationin a nonuniform slab with generalized boundary conditions and initial value is considered forgeneral cases concerned with an arbitrary nonhomogeneous medium possibly with cavity,withthe anisotropic scattering and fission,and with continuous energy varying from null to any finiteconstant or from one positive constant to another positive constant.We prove that the correspon-ding neutron transport operator A has finite Spectrum points in any strip {λ|β1≤R（?）λ≤β2}whereβ2】β1】-λ*（λ* is the essential infimum of v∑（x,v））,and obtain the asymptotic expansion ofthe time-dependent solution which exists and is unique.Furthermore,we give the existence ofthe dominant eigenvalue and indicate the asymptotic behavior of the neutron density as t→+∞.

ON THE SPECTRUM OF NEUTRON TRANSPORT OPERATOR WITH CONTINUOUS ENERGY VARYING FROM NULL TO A FINITE CONSTANT

In neutron transport theory, the strict dominance of the dominant eigenvalue associated with the transport operator plays a key role in studying the asymptotic behavior of the time dependent transport system. For bounded convex medium surrounded by vacuum, and with energy bounded away from the origin, this problem has been solved. Nevertheless, the result is only obtained under special conditions for nonhomogeneous medium with (0, v_m] energy. The general case will be discussed in this note. By the inequality given in Lemma 3, some hypotheses of [2] are weakened.

NEUMANN SERIES SOLUTION TO A NEUTRON TRANSPORT EQUATION OF SLAB GEOMETRY

This paper deals with the solution to an energy, dependent stationary neutrontransport equation of slab geometry. In L^p space, the equation is converted into an equiva-lent integral equation. By the study of the corresponding integral operator and its spectralradius, results of Neumann series solution are obtained, and an easy-verified condition thatthe transport equation has a nonnegative solution is given.

A NOTE ON THE SPECTRUM OF NEUTRON TRANSPORT OPERATOR IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α（v,μ）,γ（v,μ）and the scattering-fission kernel k（x,v,v′,μ,μ′）are boundedmeasurable,and the total collision frequency v∑（x,v）is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i（?）|β1（?）β（?）β2},where β2】β1】-λ*,with λ* the essential infimum of v∑（x,v）.Fi-nally,the asymptotic expansion of the solution for the time-dependent equation（dN）/（dt）=AN,N（0）=N0 is given as a corollary.

A SPECTRAL STREAMLINE DIFFUSION FINITE ELEMENT COUPLING METHOD OF UNSTEADY TRANSPORT EQUATION IN THE FIELD OF NEUTRON LOGGING

In this paper, a new numerical method, the coupling method of spherical harmonic function spectral and streamline diffusion finite element for unsteady Boltzmann equation in the neutron logging field, is discussed. The convergence and error estimations of this scheme are proved. Its applications in the field of neutron logging show its effectiveness.

NONLINEAR SEMIGROUP APPROACH TOTRANSPORT EQUATIONS WITH DELAYED NEUTRONS

This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.

Calculation of the reactor neutron time of flight spectrum by convolution technique

It is a very complex and time-consuming process to simulate the nuclear reactor neutron spectrum from the reactor core to the export channel by applying a Monte Carlo program. This paper presents a new method to calculate the neutron spectrum by using the convolution technique which considers the channel transportation as a linear system and the transportation scattering as the response function. It also applies Monte Carlo Neutron and Photon Transport Code （MCNP） to simulate the response function numerically. With the application of convolution technique to calculate the spectrum distribution from the core to the channel, the process is then much more convenient only with the simple numerical integral numeration. This saves computer time and reduces some trouble in re-writing of the MCNP program.

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.

A study of PFBR auxiliary neutron source strength activation and its variability with respect to the neutron spectrum and 123Sb capture cross section

In fast reactors, the inherent neutron source strength is often insufficient for monitoring the reactor start-up operation with ex-core detectors. To increase the subcritical neutron flux, an auxiliary neutron source subassembly(SSA) is generally used to overcome this problem. In this study, the estimated neutron source strength and detector count rate of an antimony-beryllium-based SSA are obtained using the deterministic transport code DORT and Monte Carlo calculations. Because the antimony activation rate is a critical parameter, its sensitivity to the capture cross section and neutron flux spectrum is studied. The reaction cross section sensitivity is studied by considering data from different evaluated nuclear data files.It is observed that, because of the variation in the cross sections from different evaluated nuclear data files, the values of the saturation gamma(> 1.67 MeV) activity and neutron strength predicted by ORIGEN2 lie within ±2%.The obtained antimony activation rate and sensitivity to the neutron flux are partially validated by irradiating samples of antimony in the KAMINI reactor. The average onegroup capture cross sections of bare and cadmium-covered 123Sb samples obtained by the ratio method are 4.0 and 1.78 b, respectively. The results of the calculation predicting the activated neutron source strength as a function of operating time and sensitivity to the neutron spectrum in the irradiation region are also presented.

Study on Sediment Transport in the Qianjiang Bay of Guang' ao, Shantou City by Using the Element Geochemistry Method

Nine samples of suspended matter at the surface or bottom and 34 elements in 20 samples of substrate sediment have been used in the neutron activation analyses. Authors study sediment and suspended matter movement by using the method of element geochemistry, and conclude through synthetic analysis and processing that the movement direction of suspended matter and substrate sediment tends to converge on the central area.

能群独立的中子输运非结构网格自适应加密

为兼顾中子输运的模拟精度和计算效率,对网格进行自适应加密和区域分解并行是有效技术途径。通常各能群的中子通量密度分布有较大差异,采用统一的网格不能最佳匹配各群通量密度的空间变化,只能全局加密网格或损失精度。本文通过对各能群中子通量密度分别进行后验误差估计,开展能群独立的局部网格加密,获得与各能群的中子通量密度分别匹配的多组非结构网格,即基于共同父网格(粗网格)的多组独立子网格(细网格),进而开发了在这种层次化父-子网格上的多群中子输运模拟耦合算法,通过连续的多轮次自适应加密,实现了不受初始网格分辨率影响的高精度、高效率求解。基于该网格方法建立了间断有限元输运程序ENTER-Ⅱ,并借助开源算法库DEAL.Ⅱ实现了区域分解并行。初步验证表明,计算结果符合良好,时间效率有明显提升。

非共振能区连续能量确定论中子输运计算方法研究

为了分析核反应堆堆芯内相关物理量分布,需要利用数值方法求解中子输运方程。其中,概率论方法计算效率尚无法满足大型工程计算的需求;而确定论方法大都采用多群近似技术,需要制作专门的多群数据库、进行复杂的共振计算。为了消除确定论方法中的多群近似,本研究提出了基于函数展开的连续能量确定论中子输运计算技术。针对核反应微观截面在非共振能区的特点,建立了多项式基函数展开技术,恰当地刻画了中子在能量维度上的耦合特性,给出了中子通量密度和核反应率等物理量随中子能量的分布。本文详细介绍了非共振能区函数展开技术的理论模型、程序开发与验证。数值结果表明,该技术思路可行。

乏燃料运输和储存容器中子屏蔽材料应用及研究现状

目的了解国内外乏燃料运输和储存容器中子屏蔽材料的类型,整理分析现有中子屏蔽材料的性能和特点,为应用于乏燃料运输和储存容器的中子屏蔽材料的研发提供一定参考。方法综述国内外应用于乏燃料运输和储存容器中子屏蔽材料的应用现状,对关键性能进行总结和比较,并提出其研究重点和发展趋势。结果目前,硼化不锈钢、碳化硼/铝复合材料、硼铝合金、聚合物基复合材料和屏蔽混凝土等中子屏蔽材料已应用于乏燃料运输和储存容器。结论随着核电厂高燃耗的发展趋势,未来乏燃料运输和储存容器对中子屏蔽材料的性能提出了更严格的要求,建议注重研发屏蔽性能优异、装配更换方便、耐辐照的中子屏蔽材料。

AB-BNCT中子输运过程的NECP-MCX软件模拟研究

硼中子俘获治疗(Boron Neutron Capture Therapy,BNCT)是国际上极具应用前景的精准治癌手段,中子输运过程直接影响着束流特性和治疗计划的准确性。研究利用新型蒙特卡罗软件NECP-MCX(Nuclear Engineering Computational Physics)开展加速器驱动硼中子俘获治疗(Accelerator Based-Boron Neutron Capture Therapy,AB-BNCT)装置的中子输运过程,计算了中子输运过程中束流整形体出口处的束流参数及不同数据库下头模中的相对生物学剂量沉积。研究结果表明:在确定的束流整形器(Beam-Shaping Assembly,BSA)设计方案下,NECP-MCX模拟计算的中子束流参数结果与主流蒙特卡罗软件计算结果偏差微小,最大参数相对误差约6%,均符合国际原子能机构(International Atomic Energy Agency,IAEA)推荐值,证实NECP-MCX可用于ABBNCT中子输运模拟研究;针对Snyder头模,使用不同数据库与NECP-MCX相匹配,计算得到的头模内相对生物剂量参数均符合临床治疗标准,考虑到ENDF/B-VⅢ.0、JENDL-5更加全面细致,建议后续AB-BNCT治疗计划系统中计算数据库选择此两种数据库。

三维球床几何稀疏条数长特征线加速方法

特征线法具有非常强的几何适应性,可用于三维球床高温气冷堆全堆芯求解,但存在迭代次数多、计算速度慢的缺点。本文将长特征线加速方法应用于三维球床高温气冷堆以解决非规则几何数值加速的问题,基于三维模型特征线布置较二维模型稠密的分析,提出了稀疏条数长特征线加速方法,极大地减少了加速方程的计算量,在不降低角度离散精度的前提下,获得了非常好的加速效果。通过基准题对加速参数的选取方式进行了研究,条数稀疏度取3~5、长特征线长度取2.0 cm左右、加速迭代步取20~60步可获得良好的加速效果。小型轻水堆三维基准题和球床堆芯简化模型的计算结果表明,采用稀疏条数长特征线加速可获得7倍左右的时间加速比,此时对应的迭代步加速比为20倍左右。