首页|The Order of Accuracy Related to the Error from Source Approximation in the Method of Characteristics for Purely Absorbing Materials in Planar Geometry
The Order of Accuracy Related to the Error from Source Approximation in the Method of Characteristics for Purely Absorbing Materials in Planar Geometry
Ji-Pu Wang Zhen-Wen Wei Can Huang William Martin Brendan Kochunas Qi-Cang Shen Si-Juan Chen Martin Pilch
The Order of Accuracy Related to the Error from Source Approximation in the Method of Characteristics for Purely Absorbing Materials in Planar Geometry
The Order of Accuracy Related to the Error from Source Approximation in the Method of Characteristics for Purely Absorbing Materials in Planar Geometry
摘要
The method of characteristics (MoC) is a well-established tool for lattice physics calculations, offering advantages such as accurate representations of both lattice geometry and boundary conditions. The flat source (FS) approximation is the most commonly used approach, while the linear source (LS) approximation enhances accuracy by preserving higher-order spatial moments of the neutron source. However, determining the order of accuracy (OoA) for spatial discretization in 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 analyze the spatial order of accuracy of 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 using the Method of Manufactured Solutions (MMS). The results demonstrate that the FS approximation achieves second-order accuracy, while the LS approximation attains fourth-order accuracy.
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