Conception of a full-core reactor model in transport theory

加拿大未来在核能方面的成功与第三代反应堆的成功设计密切相关，第三代反应堆可以降低电力成本，同时增加安全裕度。由加拿大原子能有限公司（AECL）设计的ACR-1000就是这样一种设计。稍后，第四代反应堆（Gen IV）预计将产生非常高温的蒸汽，这是制氢所需的条件。AECL提出了超临界水反应堆（SCWR）作为第四代概念。这些反应堆是减少温室效应和我们对化石燃料依赖的最重要选择。该NSERC/DG研究提案涉及开发先进的数值方法，用于为ACR-1000和高泄漏堆芯设置参考反应堆模型，该模型可作为设计超临界水反应堆的起点。本申请中提出的先进数值方法是具有三个共同特征的中子输运方程的求解技术：（1）确定性，（2）一阶输运算子和（3）超收敛。选择确定性方法将使我们能够在现有的计算机代码DRAGON V4和TRIVAC（代码DONJON V4的子集）中实现它们。一阶SN或简化PN方法使得空（或接近空）区域的表示成为可能，并且简化各向异性散射的实现。超收敛近似是那些具有原始-对偶一致性的近似，这是一种数值性质，与给定离散阶数的精度提高有关。将开发以下数值方法：（1）高阶菱形格式及其在全堆芯问题中的应用（2）用超收敛SPN方法开发三维反应堆模型（3）开发切片平衡方法及其在格点和全堆芯问题中的应用。

The future success on nuclear energy in Canada is closely related to the successful design of a third-generation reactor, permitting to lower the cost of electricity while increasing the safety margins. The ACR-1000, being designed by Atomic Energy of Canada Limited (AECL), is one such design. Later in time, fourth-generation reactors (Gen IV) are expected to produce very high temperature steam, a condition required for Hydrogen production. The AECL is proposing the Super Critical Water Reactor (SCWR) as a Gen IV concept. These reactors represent the most serious option to reduce both greenhouse effect and our dependency on fossil fuels. This NSERC/DG research proposal is related to the development of advanced numerical methods for setting reference reactor models for the ACR-1000 and for a high leakage core that could serve as a starting point for designing the SCWR. The advanced numerical methods being proposed in this application are solution techniques of the neutron transport equation with three common characteristics: (1) deterministic, (2) first-order transport operator and (3) superconvergent. Choosing deterministic approaches will enable us to implement them in the existing computer codes DRAGON V4 and TRIVAC (a subset of code DONJON V4). First order SN or Simplified PN approaches make possible the representation of voided (or close-to-void) regions and simplify the implementation of anisotropic scattering. Superconvergent approximations are those featuring primal-dual agreement, a numerical property that is related to an improvement of their accuracy for a given order of discretization. The following numerical approaches will be developed: (1) High-order diamond schemes and application to full-core problems (2) Development of 3D reactor models with the superconvergent SPN method (3) Development of the Slice Balance Approach and application to lattice and full-core problems.