发表机构
SEMO Simulation（SEMO Simulation）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非结构网格THINC/QQ重构依赖拓扑求积和牛顿迭代的问题，提出二次矩匹配S型（QMMS）近似，用闭式矩公式替代，保持精度且重构阶段提速约2倍。
AI 中文摘要
在非结构网格上，采用二次曲面表示和高斯求积的界面捕捉正切双曲（THINC/QQ）方法需要依赖于拓扑结构的数值求积来计算单元和面积分，并通过牛顿迭代求解曲面常数。本研究引入一种二次矩匹配S型（QMMS）近似，该方法从二次场的均值和方差中评估这些量，同时保留双曲正切重构剖面和边界变差减小（BVD）公式。斜率匹配的高斯累积分布函数和矩匹配的高斯模型为曲面常数和面平均值提供了闭式近似，从而消除了这些评估中的牛顿迭代和依赖拓扑结构的运行时求积。单单元测试和九个二维及三维基准测试评估了重构精度、流场差异和计算成本。在所有测试案例中，主要的输运和激波结构与使用THINC/QQ获得的结果保持紧密一致，局部差异主要集中在间断、接触区域和已发展的剪切层附近。重构阶段的性能分析给出二维和三维中THINC/QQ到QMMS的平均时间比分别为2.12和1.85。因此，QMMS降低了重构阶段的成本，同时用统一的基于矩的公式取代了依赖拓扑结构的运行时积分评估。
英文摘要
On unstructured grids, the tangent of hyperbola for interface capturing (THINC) method with quadratic surface representation and Gaussian quadrature (THINC/QQ) requires topology-dependent numerical quadrature for cell and face integrals and Newton iteration for the surface constant. This study introduces a quadratic moment-matched sigmoid (QMMS) approximation that evaluates these quantities from the mean and variance of the quadratic field while retaining the hyperbolic-tangent reconstruction profile and the boundary variation diminishing (BVD) formulation. A slope-matched Gaussian cumulative distribution function and a moment-matched Gaussian model provide closed form approximations for the surface constant and face averages, eliminating Newton iteration and topology-dependent runtime quadrature from these evaluations. Single-cell tests and nine two- and three-dimensional benchmarks assess reconstruction accuracy, flow-field differences, and computational cost. Across the tested cases, the principal transported and shock structures remain closely aligned with those obtained using THINC/QQ, with local differences concentrated mainly near discontinuities, contact regions, and developed shear layers. Reconstruction-stage profiling gives mean THINC/QQ-to-QMMS time ratios of 2.12 in two dimensions and 1.85 in three dimensions. QMMS therefore reduces reconstruction-stage cost while replacing topology-dependent runtime integral evaluation with a common moment-based formulation
