This paper presents the first application of a symmetric interior-penalty discontinuous Galerkin isogeometric analysis (SIP-DG-IGA) spatial discretization to the self-adjoint angular flux (SAAF) form of the multi-group neutron transport equation. The penalty parameters are determined, for general element types, from a mathematically rigorous coercivity analysis of the bilinear form. The proposed scheme produces a compact spatial discretization stencil. It also yields symmetric positive-definite (SPD) matrices, which can be efficiently solved using pre-conditioned conjugate gradient (PCG) solution algorithms. The proposed discretization scheme is verified using the method of manufactured solutions (MMS) and several nuclear reactor physics benchmark verification test cases. For sufficiently smooth elliptic problems, the proposed spatial discretization can exploit higher-order continuity, or k-refinement, of the NURBS basis to consistently yield greater numerical accuracy per degree of freedom (DoF) than standard h-refinement. Since this is a discontinuous scheme, it can also accurately model significant changes in the neutron scalar flux that may occur near the material interfaces of heterogeneous problems.

中文翻译：

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中子输运方程自伴角通量形式的对称内罚不连续伽辽金等几何分析空间离散


本文首次将对称内罚不连续伽辽金等几何分析 (SIP-DG-IGA) 空间离散化应用于多群中子输运方程的自伴角通量 (SAAF) 形式。对于一般元素类型，惩罚参数是根据双线性形式的数学上严格的矫顽力分析来确定的。所提出的方案产生紧凑的空间离散化模板。它还生成对称正定 (SPD) 矩阵，可以使用预条件共轭梯度 (PCG) 求解算法有效求解。使用制造解法（MMS）和几个核反应堆物理基准验证测试用例对所提出的离散化方案进行了验证。对于足够平滑的椭圆问题，所提出的空间离散化可以利用 NURBS 基础的高阶连续性或 k 细化，以一致地产生比标准 h 细化更高的每自由度 (DoF) 数值精度。由于这是一个不连续的方案，它还可以准确地模拟异质问题的材料界面附近可能发生的中子标量通量的显着变化。