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

该研究计划的长期目标是开发和实施基于输运的格点代码新的或改进的数值模拟技术，使其更精确和有效的工具来分析核反应堆中的中子行为。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。我们提出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。这款免费分发的软件在加拿大和国外用于CANDU的安全分析，并在世界各地的实验室和大学用于先进的反应堆研究。格形程序主要用于为有限堆芯计算软件提供空间均匀化和能量凝聚的截面。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中子输运模拟。然而，核反应堆是有限的，这意味着中子将从晶格中逃逸。这就是泄漏模型有用的地方，因为它们除了产生用于燃料燃耗和晶格均匀化的更具代表性的通量分布之外，还提供了在临界晶格中模拟这种效应的方法。目前，在格型代码中实现的最先进的异质泄漏方法是简化的异质B1模型，但其使用仅限于完全反射对称2D几何形状（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在DRAGON中编程的特征线法（MoC）可以求解高阶角通量模式的输运方程来开发非均匀BN泄漏模型。作为第一步，我们将实施，我的学生和我，在DRAGON中使用MoC在完全反射的非对称2D几何形状中使用先进的B1异质泄漏方法。对于第二步，工作将继续推广BN方法的三维几何形状与混合边界条件（轴向空隙和径向白色反射）。第三，我们将开发一个三维循环跟踪程序，使镜像反射边界条件可以处理在三维输运解决方案。这将通过消除导致外部边界处存在小表面的计算损失来大幅提高DRAGON的3D模拟性能。最后，我们将提出并实施一个先进的加速技术，三维全核心蒙特卡罗模拟。这将基于一种迭代算法来求解细网格MoC方程，其中输入角通量边界条件由粗网格Monte Carlo模拟生成。**

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.**