AI 中文总结
本文针对多面体网格上离散纵标输运的高阶迎风间断伽辽金离散，提出输运匹配的修正内罚校正，实现源迭代的严格加速，数值实验验证了收敛性与缩放关系。
AI 中文摘要
扩散合成加速的有效性取决于其扩散校正是否反映产生迭代误差的输运离散。本文针对多面体网格上离散纵标输运的高阶迎风间断伽辽金离散，发展了该原理。从离散输运扫描中，推导了可一步消除源迭代标量误差的精确标量校正；证明了相关标量响应是正定且自伴的，得到了源迭代收敛因子的精确表达式，并量化了真空泄漏产生的额外阻尼。以精确校正为参考，构造了输运匹配的修正内罚校正，其边界项直接继承自均匀真空流入。在光学厚区，所得MIP形式近似精确校正的相对误差与有效单元克努森数成正比，这实现了源迭代的严格加速，且对于可接受的多面体网格，其界在网格尺寸、多项式次数及单元面数上是一致的。在笛卡尔网格和质心Voronoi网格上的数值实验证实了预测的收敛性和校正算子的缩放关系。
英文摘要
Diffusion synthetic acceleration is most effective when its diffusion correction reflects the transport discretisation that generates the iteration error. We develop this principle for high-order upwind discontinuous Galerkin discretisations of discrete-ordinates transport on polytopic meshes. From the discrete transport sweep, we derive the exact scalar correction that removes the source-iteration scalar error in one step. We prove that the associated scalar response is positive and self-adjoint, obtain an exact expression for the source-iteration convergence factor, and quantify the additional damping produced by vacuum leakage. Using the exact correction as a reference, we construct a transport-matched modified interior penalty correction whose boundary terms are inherited directly from homogeneous vacuum inflow. In the optically thick regime, the resulting MIP form approximates the exact correction with relative error proportional to the effective cell Knudsen number. This gives a strict acceleration of source iteration, with bounds uniform in mesh size, polynomial degree, and element face count for admissible polytopic meshes. Numerical experiments on Cartesian and centroidal Voronoi meshes confirm the predicted convergence and correction-operator scaling.
Comments25 pages, 3 figures
