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

这一研究计划的长期目标是在基于传输的格子程序中开发和实施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更有效的工具。这意味着：开发新的计算模型来处理更复杂的系统；编程健壮的方法来加速大型中子输运问题的求解算法；以及开发受益于计算机技术最新进展的计算方案。我们建议的大部分开发将在我们在蒙特利尔理工学院开发的代码Dragon中实现。这一免费分布的软件在加拿大和国外用于CANTUS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。*格子代码主要用于为有限堆芯计算软件提供空间均匀和能量浓缩的截面。对于目前运行的反应堆，这意味着在全反射燃料组件上进行2D或3D中子传输模拟。然而，核反应堆是有限的，这意味着中子将从晶格中逸出。这就是泄漏模型有用的地方，因为除了生成更具代表性的通量分布以用于燃料燃耗和晶格均质化之外，它们还提供了一种在关键晶格中模拟这种效果的方法。目前，格子程序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，但它的使用仅限于全反射对称二维几何结构(轴向无限大单元)中的碰撞概率(CP)方法。*本研究计划的短期目标是利用Dragon编程的特征线法(MOC)可以求解高阶角通量模式的输运方程，从而发展非均质BN泄漏模型。作为第一步，我和我的学生们将在Dragon中实现一个先进的B1非均匀渗漏方法，使用全反射非对称2D几何中的MOC。对于第二步，将继续将BN方法推广到具有混合边界条件(轴向空洞和径向白色反射)的3D几何图形。第三，我们将开发一个3D循环跟踪程序，以便在3D传输解中处理镜面反射边界条件。这将大大提高Dragon在3D模拟中的性能，因为它消除了由于外部边界存在小曲面而导致的计算惩罚。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细网格MOC方程，该方程带有由粗网格蒙特卡罗模拟产生的入射角通量边界条件。

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.**