Development of advanced leakage models for lattice calculations based on the method of characteristics.

本研究项目的长期目标是开发和实现基于输运晶格码的新的或改进的数值模拟技术，使其成为分析核反应堆中中子行为的更精确和有效的工具。这意味着：开发新的计算模型来处理更复杂的系统；编程鲁棒法加速大中子输运问题求解算法利用计算机技术的最新进展开发计算方案。我们提出的大部分开发将在我们在蒙特利尔理工大学开发的代码DRAGON中实现。这个免费分发的软件在加拿大和国外用于candu的安全分析，以及在世界各地的实验室和大学用于先进的反应堆研究。***格码主要用于为有限芯计算软件提供空间均质化和能量凝聚的截面。对于目前运行的反应堆，这意味着在完全反射的燃料组件上进行二维或三维中子输运模拟。然而，核反应堆是有限的，这意味着中子会从晶格中逸出。这就是泄漏模型有用的地方，因为除了产生用于燃料燃烧和晶格均匀化的更具代表性的通量分布外，泄漏模型还提供了在临界晶格中模拟这种效应的平均值。目前，在格码中实现的最先进的非均质泄漏方法是简化的非均质B1模型，但其应用仅限于全反射对称二维几何（轴向无限单元）中的碰撞概率（CP）方法。***本研究计划的短期目标是利用DRAGON中编写的特性方法（MoC）可以求解高阶角通量模式的输运方程，建立非均相BN泄漏模型。作为第一步，我和我的学生将在DRAGON中使用完全反射非对称二维几何形状的MoC实现先进的B1异质泄漏方法。第二步，工作将继续将BN方法推广到具有混合边界条件的三维几何形状（轴向为空，径向为白反射）。第三，我们将开发一个3D循环跟踪程序，以便可以在3D传输解决方案中处理镜像反射边界条件。这将通过消除由于在外部边界存在小表面而导致的计算惩罚，大大提高DRAGON的3D模拟性能。最后，我们将提出并实现一种先进的三维全核蒙特卡罗模拟加速技术。这将基于一种迭代算法来求解由粗网格蒙特卡罗模拟生成的具有入射角通量边界条件的细网格MoC方程

The long-term objectives of this research program are to develop and implement in transport based lattice codes new or improved numerical simulation techniques to make them more precise and efficient tool to analyse neutrons behaviour in nuclear reactor. This implies: developing new computational models to treat more complex systems; programming robust method to accelerate the solution algorithm for large neutron transport problems; and developing computation schemes benefiting from recent advances in computer technology. Most of the development we proposed will be implemented in the code DRAGON we developed at Polytechnique Montreal. This freely distributed software is used in Canada and abroad for the safety analysis of CANDUs as well as in Laboratories and Universities throughout the world for advanced reactor studies.***Lattice codes are mainly used to provide spatially homogenized and energy condensed cross sections for finite core calculation software. For currently operating reactors, this implies performing 2D or 3D neutron transport simulations over fully reflected fuel assemblies. However, nuclear reactors are finite which means neutron will escape from the lattices. This is where leakage models are useful because they provide a mean to simulate this effect in a critical lattice in addition to producing a more representative flux distribution to use for fuel burnup and lattice homogenization. Currently, the most advanced heterogeneous leakage method implemented in lattice codes is the simplified heterogeneous B1 model but its use is limited to the collision probability (CP) method in fully reflected symmetric 2D geometries (axially infinite cell).***The short-term goal of this research program is to take advantage of the fact that the method of characteristics (MoC) programmed in DRAGON can solve the transport equation for high order angular flux modes to develop the heterogeneous BN leakage model. As a first step we will implement, my students and I, an advanced B1 heterogeneous leakage method in DRAGON using the MoC in fully reflected non-symmetric 2D geometries. For the second step, work will proceed on generalizing the BN method to 3D geometries with mixed boundary conditions (void axially and white reflection radially). Thirdly, we will develop a 3D cyclic tracking procedure so that mirror like reflection boundary conditions can be treated in the 3D transport solution. This will increase substantially the performance of DRAGON for 3D simulations by removing the computational penalties resulting to the presence of small surfaces at external boundaries. Finally we will propose and implement an advanced acceleration techniques for 3-D full core Monte Carlo simulations. This will be based on an iterative algorithm to solve the fine mesh MoC equation with incoming angular flux boundary conditions generated by a coarse mesh Monte Carlo simulation.**