稳态多尺度流动模拟UGKWP方法中严格论证的局部时间步长

中文摘要 AI 辅助

在本快报中，局部时间步长（LTS）被纳入统一气体动力学波粒子（UGKWP）方法用于稳态多尺度流动模拟。相对于全局时间步长（GTS），它将收敛步数加快了3.8倍至20倍，壁钟时间最多减少了21倍。对LTS下粒子通量的严格分析表明，每个单元格固定为Δti是时间平均通量平衡的充分条件。结合单元格界面处粒子质量和自由传输时间的比例缩放，固定Δti条件产生了一个无自由参数的保守框架。UGKWP-LTS方法在具有多尺度流动特征的圆柱和平板基准上得到了验证。

英文摘要

Local time stepping (LTS) can accelerate convergence to steady states in kinetic simulations with large variations in the local time steps across the computational domain. When neighboring cells advance with unequal time steps, the time-averaged particle flux must be balanced across their common interface. For particle-based or hybrid wave-particle methods under finite volume method (FVM) framework, we rigorously establish a sufficient condition for time-averaged interfacial particle-flux balance: fixed positive local time steps together with proportional particle-mass scaling. When a particle crosses from cell $L$ to cell $R$, its mass is scaled by $Δt_R/Δt_L$. In the unified gas-kinetic wave-particle (UGKWP) implementation, the same ratio is applied to the remaining free-transport time of the crossing particle. LTS also affects the wave-particle decomposition and the time integration of the wave fluxes in UGKWP. The wave-particle decomposition in cell \(i\) is determined by the local ratio \(Δt_i/τ_i\), which better reflects the local relation between the observation scale and relaxation time for multiscale cases. The equilibrium and analytic free transport wave fluxes are integrated over and normalized by the corresponding cell-side time steps to obtain the interfacial time-averaged wave fluxes. The UGKWP-LTS method is used to simulate the hypersonic flow past a cylinder at $\mathrm{Kn}=0.01$ and $0.1$, and a flat plate at $\mathrm{Kn}=0.0169$. In all three cases, the surface quantities obtained with UGKWP-LTS agree well with the reference data. Relative to global time stepping (GTS), UGKWP-LTS achieves step-count speedups of $6.6\times$, $3.8\times$, and $20\times$ for the three cases, respectively. The corresponding wall-clock speedups are $7.1\times$, $4.5\times$, and approximately $21\times$.

发表机构

• Hong Kong University of Science and Technology（香港科技大学）
• HKUST Shenzhen Research Institute（香港科技大学深圳研究院）

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