AI 中文总结
研究为固定 D3Q125 离散速度动力学公式开发分层阶次分辨松弛模型，结合宏观梯度背景与不同阶次非平衡指标定义有效量，经多种测试验证其有效性，能降低非平衡强度，建立了阶次分辨激活机制及数值行为。
AI 中文摘要
我们为固定的 D3Q125 离散速度动力学公式开发了一种分层阶次分辨松弛模型。传统的自适应碰撞模型通常对所有保留的矩阶使用一个标量稀疏或非平衡指标，从而耦合不同的动力学扇区。在此，一个共享的宏观梯度背景分别与二阶、三阶和四阶热力学非平衡指标相结合，以定义有效量 K2、K3 和 K4，每个都驱动其自己的对数高斯松弛谱。纯阶次微扰测试验证了选择性激活，不匹配的扇区保持在舍入水平。均匀混合阶次、幅度和成分测试表明，在保持正种群的同时，残余非平衡低于普通传感器模型。在规定的参考离散化下的平滑周期压缩波中以及在仅 TNE 传感器极限中，峰值总非平衡强度降低了 6.565%，在整个域和所有保留的矩扇区都有降低。额外的时间步长、输运离散化、松弛谱、均匀升压、长时间和剪切波研究表明，分层校正的符号在测试配置中是稳健的，而其幅度取决于时间步长、输运方案、传感器框架和松弛谱。周期基准将主要全局不变量保持到浮点精度并保持正值。这些结果建立了固定速度集上阶次分辨激活的机制和数值行为；在声称普遍提高精度之前，仍需要独立的动力学参考验证。
英文摘要
We develop a hierarchical order-resolved relaxation model for a fixed D3Q125 discrete-velocity kinetic formulation. Conventional adaptive collision models often use one scalar rarefaction or nonequilibrium indicator for all retained moment orders, thereby coupling distinct kinetic sectors. Here, a shared macroscopic-gradient background is combined separately with second-, third-, and fourth-order thermodynamic nonequilibrium indicators to define effective measures K2, K3, and K4, each driving its own log-Gaussian relaxation spectrum. Pure-order perturbation tests verify selective activation, with nonmatching sectors remaining at roundoff level. Homogeneous mixed-order, amplitude, and composition tests show lower residual nonequilibrium than a common-sensor model while preserving positive populations. In a smooth periodic compression wave at the stated reference discretization and in the TNE-only sensor limit, the peak total nonequilibrium intensity is reduced by 6.565%, with reductions throughout the domain and in all retained moment sectors. Additional timestep, transport-discretization, relaxation-spectrum, uniform-boost, long-time, and shear-wave studies show that the sign of the hierarchical correction is robust over the tested configurations, while its magnitude depends on timestep, transport scheme, sensor frame, and relaxation spectrum. Quantitative boost checks identify the laboratory-frame raw-Hermite origin of the frame sensitivity without detecting an evident collision-path inconsistency over the tested range. The periodic benchmarks preserve the principal global invariants to floating-point accuracy and remain positive. These results establish the mechanism, selectivity, and numerical behavior of order-resolved activation on a fixed velocity set; independent kinetic-reference validation is still required before claiming universal accuracy improvement.
Comments63 pages, 8 figures, 7 tables. v2 adds frame-dependence validation and additional numerical sensitivity and refinement studies; the core model is unchanged
