Delta-form-based methods for solving high order spatial discretization schemes are introduced into the reactor S_N transport equation. Due to the nature of the delta-form, the final numerical accuracy only depends on the residuals on the right side of the discrete equations and have nothing to do with the parts on the left side. Therefore, various high order spatial discretization methods can be easily adopted for only the transport term on the right side of the discrete equations. Then the simplest step or other robust schemes can be adopted to discretize the increment on the left hand side to ensure the good iterative convergence. The delta-form framework makes the sweeping and iterative strategies of various high order spatial discretization methods be completely the same with those of the traditional S_N codes, only by adding the residuals into the source terms. In this paper, the flux limiter method and weighted essentially non-oscillatory scheme are used for the verification purpose to only show the advantages of the introduction of delta-form-based solving methods and other high order spatial discretization methods can be also easily extended to solve the S_N transport equations. Numerical solutions indicate the correctness and effectiveness of delta-form-based solving method.

将用于求解高阶空间离散化方案的基于 Delta 形式的方法引入到反应堆 S _N输运方程中。由于 delta 形式的性质，最终的数值精度仅取决于离散方程右侧的残差，与左侧的部分无关。因此，对于离散方程右侧的输运项，可以很容易地采用各种高阶空间离散化方法。然后可以采用最简单的步骤或其他鲁棒方案对左侧的增量进行离散化，以确保良好的迭代收敛。delta-form框架使得各种高阶空间离散化方法的扫描和迭代策略与传统S的完全相同。_{N 个}代码，只需将残差添加到源项中即可。在本文中，通量限制器方法和加权本质上非振荡方案用于验证目的，仅显示引入基于delta形式的求解方法的优点，其他高阶空间离散化方法也可以很容易地扩展到求解 S _N传输方程。数值解表明了基于delta形式的求解方法的正确性和有效性。