Abstract The recently developed linear prolongation Coarse Mesh Finite Difference (lpCMFD) acceleration scheme, which employs a linear additive approach to update the scalar flux, has been shown to be more stable and effective than the conventional scaling-based Coarse Mesh Finite Difference (CMFD) method for accelerating the discrete ordinates (SN) neutron transport calculation using spatial finite difference discretization. In this paper, we study and extend the application of lpCMFD to accelerate the SN neutron transport calculation with spatial discretization using the Discontinuous Galerkin Finite Element Method (DGFEM), which generally involves linear- or higher-order space expansion functions. A function space mapping operator is proposed in this paper to project the lpCMFD linear-order correction flux to an arbitrary-order DGFEM basis function, which is implemented and tested on a one-dimensional (1-D) in-house–developed DGFEM-based SN code. The consistency between the lpCMFD accelerated results and the pure SN results is naturally guaranteed by employing upwind current information from DGFEM-based SN transport calculation to evaluate the drift coefficient. It was found from our numerical testing with the CMFD and the lpCMFD acceleration schemes on single-group fixed-source and k-eigenvalue problems that both acceleration schemes can reproduce the unaccelerated scalar flux and keff, respectively. Further numerical testing on a more realistic case is performed on a 1-D slice multi-energy-group problem based on the three-dimensional C5G7 mixed oxide (MOX) benchmark. It was found that by using the function space projector proposed in this paper, lpCMFD was stable and effective to accelerate the DGFEM-based SN neutron transport calculation for all coarse mesh sizes tested while CMFD diverged for large optical thickness.

中文翻译：

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基于不连续伽辽金有限元法计算离散纵坐标中子输运​​的线性扩展粗网格有限差分加速度

摘要 最近开发的线性延长粗网格有限差分 (lpCMFD) 加速方案采用线性加法方法来更新标量通量，已被证明比传统的基于缩放的粗网格有限差分 (CMFD) 更稳定和有效使用空间有限差分离散化加速离散纵坐标 (SN) 中子输运计算的方法。在本文中，我们研究并扩展了 lpCMFD 的应用，以使用不连续伽辽金有限元方法 (DGFEM) 进行空间离散化来加速 SN 中子输运计算，该方法通常涉及线性或高阶空间扩展函数。本文提出了一种函数空间映射算子，将 lpCMFD 线性阶校正通量投影到任意阶 DGFEM 基函数，该函数在内部开发的一维 (1-D) DGFEM 基函数上实现和测试。基于SN码。lpCMFD加速结果和纯SN结果之间的一致性通过采用基于DGFEM的SN输运计算的逆风流信息来评估漂移系数自然得到保证。从我们使用 CMFD 和 lpCMFD 加速方案对单组固定源和 k 特征值问题的数值测试中发现，两种加速方案都可以分别再现未加速的标量通量和 keff。对基于三维 C5G7 混合氧化物 (MOX) 基准的一维切片多能组问题进行了更真实案例的进一步数值测试。发现通过使用本文提出的函数空间投影仪，lpCMFD 稳定且有效地加速所有测试的粗网格尺寸的基于 DGFEM 的 SN 中子传输计算，而 CMFD 发散为大光学厚度。