蒙特卡罗（MC）方法和确定论方法是中子输运计算的两类重要方法。蒙卡方法的优点是能够准确描述和处理复杂物理系统，减少因近似引起的建模和计算误差。随着新型核能系统和计算机硬件的发展，蒙卡方法成为国际研究热点。燃耗计算和源收敛问题是蒙卡研究领域两个颇具挑战性的难题，同时又分别是反应堆分析设计的核心基础需求和蒙卡方法提高效率和保证计算准确度的关键。本课题基于自主堆用蒙卡程序RMC，对蒙卡燃耗和源收敛问题开展研究。蒙卡燃耗计算是蒙卡输运计算和点燃耗计算的相互耦合。传统的蒙卡燃耗程序一般通过开发第三方接口，外耦合调用蒙卡程序（如MCNP）和点燃耗程序（如ORIGEN），其计算能力通常局限于栅元、组件等小规模燃耗问题。本课题研究了燃耗计算新方法，开发了RMC内耦合燃耗计算功能，发展了其大规模问题燃耗计算能力。首先，研究了复杂核素系统的点燃耗算法，包括线性子链分析和矩阵指数法，开发验证了点燃耗计算程序DEPTH。然后，通过内耦合RMC与DEPTH，实现RMC燃耗计算功能，并改进能量查找和单群截面统计方法；通过基准题计算以及与其它参考程序的比较，验证了RMC燃耗功能的正确性。特别地，课题研究了大规模蒙卡燃耗计算方法，包括重复结构燃耗区自动展开、大规模栅元快速统计、蒙卡大规模并行效率优化和点燃耗并行计算；通过计算二维压水堆全堆燃耗问题，验证了RMC的大规模燃耗计算能力，并研究了燃耗功率振荡问题。源收敛问题是蒙卡方法面临的长期性难题。本课题将蒙卡源收敛问题按照慢收敛、低抽样和方差低估计三类子问题分别开展研究。针对蒙卡慢收敛问题，课题研究了蒙卡源迭代的理论模型，并发现已有研究结论的不合理之处；证明了常规维兰德和超历史加速方法不能减少蒙卡源收敛计算时间，继而提出渐近维兰德方法和渐近超历史方法。针对蒙卡低抽样问题，研究了低抽样的产生机理和表现形式；提出基于裂变矩阵的低抽样诊断方法，该方法具有较强的普适性和易操作性。针对方差低估计问题，研究了方差低估计机理和现象；采用组统计方法修正计数器当中的方差低估计偏差，并提出确定每组中子代数的简便方法；此外，研究了计算占优比的裂变矩阵法和噪声传递矩阵法。本课题不仅在蒙卡燃耗和源收敛问题的方法创新和算法实践方面取得突破，而且使得RMC程序在若干关键技术和功能上达到先进水平。
The Monte Carlo (MC) method and the deterministic method are two essential methods for neutron transport calculations. In comparison to the deterministic method, the MC method has advantages in treating complex physical systems with less approximations and subsequent higher accuracy. With the development of new conceptual nuclear systems and computer technologies, the MC method is obtaining rising attentions in worldwide. Burnup calculations and fission source convergence are two challenging problems for the MC method. This work investigates the MC burnup calculation and source convergence problems by using the self-developed Monte Carlo code RMC.The MC burnup calculation is a coupling of the MC transport calculation and the point-depletion calculation. Conventional MC burnup codes are mostly interfaces explicitly linking MC transport codes (i.e. MCNP) and point-depletion code (i.e. ORIGEN), which are usually limited to small-scale burnup problems such as pin-level or assembly-level calculations. In this work, the RMC built-in burnup function is developed, and is extended to large-scale burnup calculations. Firstly, based on research on point-depletion algorithms including Transmutation Trajectory Analysis (TTA) and matrix exponential method, a point-depletion code DEPTH is developed and validated. Secondly, the RMC burnup function is realized by implicitly coupling the DEPTH module, and it is further optimized by using the new energy-bin method and one-group cross-section tally method. The RMC burnup capabilities are validated by benchmark calculations and comparisons to reference codes. Thirdly, various methods for MC large-scale burnup calculations are proposed and implemented in the RMC code. A 2D PWR full-core burnup case is calculated to show RMC’s capability in large-scale burnup cases. Besides, the power oscillation in MC burnup calculations is investigated.Fission source convergence has long been a challenge for MC criticality calculations. This work studies three forms of MC convergence problems, that is, the slow source convergence, the undersampling, and the bias underprediction. Firstly, the theoretical model of MC power iteration is analyzed and examined to find some unreasonable conclusions made by previous studies. It is proved that the conventional Wielandt method and the super-history method are not able to reduce computational time for source convergence, and consequently, the asymptotic Wielandt method and the asymptotic super-history method are proposed. Secondly, by analyzing the mechanism and phenomenons of MC undersampling, a robust method based on fission matrix is proposed for undersampling diagnostics. Thirdly, as for the bias underprediction problem, the batch method is used to calculate the real variance of local tallies, and a convenient way of deciding the batch size is proposed. Besides, the fission matrix method and the noise propagation matrix method for calculating the dominance ratio are investigated.The thesis has not only provide new methods and valuable practice for MC burnup and fission source convergence, but also significantly enhanced some crucial capabilities of the RMC code.
