用于 D3Q125 上帧鲁棒阶分辨弛豫的中心厄米特传感与碰撞
Central-Hermite Sensing and Collision for Frame-Robust Order-Resolved Relaxation on D3Q125
AI总结：
研究针对 D3Q125 动力学模型，开发中心厄米特公式并比较三种变体。通过实验发现模型 C 在保持模态纯度、降低碰撞帧差异方面表现出色，虽有残余依赖性，但能减少碰撞引起的交叉阶帧差异，不过宏观传输误差降低效果待进一步验证。
AI中文摘要：
在固定离散速度集上的原始厄米特传感和碰撞可将均匀平移转化为名义上不同的非平衡阶之间的人工耦合。我们为具有阶分辨对数高斯弛豫的 D3Q125 动力学模型开发了一种中心厄米特公式，并比较了三个变体：原始传感/原始碰撞（A）、中心传感/原始碰撞（B）和中心传感/中心碰撞（C）。在均匀平移的二阶扰动中，模型 C 在机器精度下保持三阶和四阶模态纯度，而 A 和 B 会产生与推进相关的交叉阶内容。在整个网格 - CFL - 推进矩阵中，模型 C 相对于 A 在总相对 L - 无穷范数度量中，将传输后碰撞帧差异降低了 65.342 - 98.102%（中位数 81.131%）。长时间计算在数值精度上保持正值和守恒性，尽管累积收益取决于配置，因为传输不断重新注入帧误差。传输研究进一步揭示了一个明显的权衡：中心厄米特界面重建强烈抑制三阶差异，但放大四阶差异。因此，完全的中心厄米特碰撞大大减少了碰撞引起的交叉阶帧差异，而由于离散传输和有限速度空间表示，仍存在残余依赖性。这种矩空间的改进本身并不能在宏观伽利略传输误差上实现可比的降低。
英文摘要：
Raw-Hermite sensing and collision on a fixed discrete-velocity set can convert a uniform translation into artificial coupling between nominally distinct nonequilibrium orders. We develop a central-Hermite formulation for a D3Q125 kinetic model with order-resolved log-Gaussian relaxation and compare three variants: raw sensing/raw collision (A), central sensing/raw collision (B), and central sensing/central collision (C). In homogeneous translated second-order perturbations, model C preserves third- and fourth-order modal purity to machine precision, whereas A and B develop boost-dependent cross-order content. Across a grid-CFL-boost matrix, model C reduces the post-transport collision frame discrepancy relative to A by 65.342-98.102% (median 81.131%) in the total relative L-infinity measure. Long-time calculations remain positive and conservative to numerical precision, although the accumulated benefit is configuration dependent because transport continually re-injects frame error. A transport study further reveals a clear trade-off: central-Hermite interface reconstruction strongly suppresses the third-order discrepancy but amplifies the fourth-order discrepancy. The fully central-Hermite collision therefore substantially reduces collision-induced cross-order frame discrepancy, while residual dependence remains due to discrete transport and finite velocity-space representation. This moment-space improvement does not by itself establish a comparable reduction in macroscopic Galilean transport error.
