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<p>The method of characteristics (MoC) is a well-established tool for lattice physics calculations, offering advantages such as accurate representation of both lattice geometry and boundary conditions. The flat source (FS) approximation is the most commonly used approach, whereas the linear source (LS) approximation enhances the accuracy by preserving the higher-order spatial moments of the neutron source. However, determining the order of accuracy (OoA) for spatial discretization in the MoC is challenging, particularly for the LS approximation. This complexity arises because MoC employs two spatial meshes: the fission source region (FSR) mesh and a set of characteristic rays used to integrate the transport equation over the FSR mesh. In this study, we analyzed the spatial order of accuracy of the MoC in planar geometry for both FS and LS approximations in relation to the distributed source. Our theoretical predictions are consistent with the numerical results obtained using the Method of Manufactured Solutions (MMS). The results demonstrate that the FS approximation achieves second-order accuracy, whereas the LS approximation attains fourth-order accuracy.</p>

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The order of accuracy related to the error from source approximation in the method of characteristics for purely absorbing materials in planar geometry

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Ji-Pu Wang,
  • Zhen-Wen Wei,
  • Can Huang,
  • William Martin,
  • Brendan Kochunas,
  • Qi-Cang Shen,
  • Si-Juan Chen,
  • Martin Pilch

摘要

The method of characteristics (MoC) is a well-established tool for lattice physics calculations, offering advantages such as accurate representation of both lattice geometry and boundary conditions. The flat source (FS) approximation is the most commonly used approach, whereas the linear source (LS) approximation enhances the accuracy by preserving the higher-order spatial moments of the neutron source. However, determining the order of accuracy (OoA) for spatial discretization in the MoC is challenging, particularly for the LS approximation. This complexity arises because MoC employs two spatial meshes: the fission source region (FSR) mesh and a set of characteristic rays used to integrate the transport equation over the FSR mesh. In this study, we analyzed the spatial order of accuracy of the MoC in planar geometry for both FS and LS approximations in relation to the distributed source. Our theoretical predictions are consistent with the numerical results obtained using the Method of Manufactured Solutions (MMS). The results demonstrate that the FS approximation achieves second-order accuracy, whereas the LS approximation attains fourth-order accuracy.