发表机构
School of Mathematics and Computational Science, Xiangtan University; National Center for Applied Mathematics in Hunan; Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University（湘潭大学数学与计算科学学院; 湖南省应用数学中心; 湘潭大学计算与工程科学湖南省重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出宏观阴影校正格子玻尔兹曼方法（MSC-LBM），通过缺陷校正消除声学时间步长限制，实现低雷诺数瞬态流动的快速时间精确模拟，在匹配精度下获得最高122倍加速。
AI 中文摘要
显式格子玻尔兹曼方法对慢瞬态流动的模拟受到声学时间步长的限制。双时间步进可以消除这一限制，但缓慢的内部收敛使得已报道的墙钟加速比仅约为四到十倍，且缺乏随网格细化而增强的机制。我们提出了宏观阴影校正格子玻尔兹曼方法（MSC-LBM），该方法对未分裂的动力学残差应用缺陷校正。在每个傅里叶波数下，对守恒残差矩精确求解类斯托克斯系统，同时保持二阶后向差分公式（BDF2）的固定点及时间精度。在双松弛时间轴Λ=1/4上，ω⁺=ω⁻=1使得一次碰撞消除所有非流体动力学扰动；η(ν)=|6ν-1|/(6ν+1)在ν=1/6时为零，留下流体动力学慢模，其长波阴影由校正器反转。在完成的计时测试中，MSC-LBM在N=256、Re=1条件下，在匹配精度和1%误差门限下分别实现27.95倍和52.71倍的墙钟加速。匹配加速比在N=1024时单调上升至122.02，且在Re=10⁻⁴至100范围内持续保持增益。三维D3Q19扩展在N=128、Re=1时，在相同门限下分别达到27.85和8.84。结合反弹一致性的动力学粗求解器与自适应重线性化，将MSC-LBM扩展至完全封闭腔体，在N=128时，Re=10和Re=100下分别获得26.86和3.84的（排除设置时间的）物理推进加速比。精确的逐波数符号逆确立了可实现的非设计工况收缩包络。收缩、参数扫描和计时结果共同界定了所展示的运行范围：低至中等雷诺数瞬态流动，其中声学步进不必决定计算成本。
英文摘要
Explicit lattice Boltzmann simulations of slow transient flows are constrained by the acoustic time step. Dual-time stepping can remove this restriction, but slow inner convergence has limited reported wall-clock gains to roughly four- to tenfold, without a mechanism that strengthens under refinement. We present the macroscopic-shadow-corrected lattice Boltzmann method (MSC-LBM), which applies defect correction to the unsplit kinetic residual. At each Fourier wavenumber, a Stokes-like system is solved exactly for the conserved residual moments while preserving the second-order backward-differentiation formula (BDF2) fixed point and temporal accuracy. Along the two-relaxation-time axis $Λ=1/4$, $ω^+=ω^-=1$ makes one collision eliminate all non-hydrodynamic perturbations; $η(ν)=|6ν-1|/(6ν+1)$ vanishes at $ν=1/6$, leaving hydrodynamic slow modes whose long-wave shadow is inverted by the corrector. In completed timing campaigns, MSC-LBM achieves 27.95- and 52.71-fold wall-clock speedups at $N=256$, $\mathrm{Re}=1$ under matched-accuracy and $1\%$ gates. The matched speedup rises monotonically to 122.02 at $N=1024$, with gains persisting across $\mathrm{Re}=10^{-4}$--$100$. The three-dimensional D3Q19 extension reaches 27.85 and 8.84 under the same gates at $N=128$, $\mathrm{Re}=1$. A bounce-back-consistent kinetic coarse solver with adaptive relinearisation extends MSC-LBM to fully enclosed cavities, yielding setup-excluding physical-march speedups of 26.86 at $\mathrm{Re}=10$ and 3.84 at $\mathrm{Re}=100$ for $N=128$. An exact per-wavenumber symbol inverse establishes the attainable off-design contraction envelope. The contraction, parameter-sweep, and timing results jointly delimit the demonstrated operating regime: low-to-moderate-Reynolds-number transients for which acoustic stepping need not dictate computational cost.
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