arXiv 2602.136012026-02physics.flu-dyn

通过深度学习加速的Lennard-Jones DSMC解决低温与高超声速稀薄流动问题

Resolving Cryogenic and Hypersonic Rarefied Flows via Deep Learning-Accelerated Lennard-Jones DSMC

Ferdowsi University of Mashhad（马什哈德 Ferdowsi 大学）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Institute of Mechanics, Bulgarian Academy of Sciences（保加利亚科学院力学研究所）

Ahmad Shoja Sani, Ehsan Roohi, Stefan Stefanov

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AI总结：

本研究通过发展基于Lennard-Jones势的DSMC框架，结合广义碰撞选择模型和深度算子网络加速散射角计算，解决了低温与高超声速稀薄流动中的物理精度与计算效率问题。

摘要：

将物理真实的Lennard-Jones (LJ) 势能集成到直接模拟蒙特卡洛 (DSMC) 中仍然具有挑战性，因为长程势能使得碰撞率定义复杂化，并导致重复散射角评估成本高昂。本研究围绕两个方法论进展和由此产生的碰撞核的输运级验证，开发了一个LJ-DSMC框架。首先，通过从局部Chapman-Enskog粘度匹配获得的变有效直径 (VED) 模型，为Bird的DSMC算法 (DSMC1, DSMC1S 和 DS2V) 制定了一个广义的碰撞选择处理方法。这种粘度一致的配对选择模型为LJ势能提供了有限的DSMC碰撞率闭合，并在氦气和氩气正激波、低温超声速Couette流以及高超声速圆柱绕流中得到了验证。结果表明，在高温排斥区域与VHS一致，但当吸引力变得重要时，显示出明显的LJ效应，包括减小的剪切应力和更大的低温尾迹。其次，通过训练深度算子网络 (DeepONet) 从高保真散射数据预测LJ偏转角，取代了数值Matsumoto-Koura积分，同时保留了标准弹性碰撞后更新，从而消除了公认的LJ二元散射步骤的计算瓶颈。该代理模型给出了平均包裹角误差为 \(1.6\times10^{-3}\,\mathrm{rad}\) 和99百分位误差为 \(9.9\times10^{-3}\,\mathrm{rad}\)，将碰撞子程序加速了40%，并将总壁钟时间减少了36%。最后，相同的DeepONet-LJ散射核在粘度控制流之外通过扩散基准进行了测试。

英文摘要：

Integrating the physically realistic Lennard--Jones (LJ) potential into Direct Simulation Monte Carlo (DSMC) remains challenging because the long-range potential complicates collision-rate definition and makes repeated scattering-angle evaluation expensive. This study develops an LJ--DSMC framework built around two methodological advances and a transport-level validation of the resulting collision kernel. First, a generalized collision-selection treatment is formulated for Bird's DSMC algorithms (DSMC1, DSMC1S, and DS2V) through a Variable Effective Diameter (VED) model obtained from local Chapman--Enskog viscosity matching. This viscosity-consistent pair-selection model provides a finite DSMC collision-rate closure for the LJ potential and is validated in helium and argon normal shocks, cryogenic supersonic Couette flow, and hypersonic cylinder flows. The results show agreement with VHS in high-temperature repulsive regimes, but reveal clear LJ effects, including reduced shear stress and larger cryogenic wakes, when attractive forces become important. Second, the computational bottleneck of the accepted LJ binary-scattering step is removed by training a Deep Operator Network (DeepONet) to predict the LJ deflection angle from high-fidelity scattering data, replacing the numerical Matsumoto--Koura integral while preserving the standard elastic post-collision update. The surrogate gives a bulk mean wrapped-angle error of \(1.6\times10^{-3}\,\mathrm{rad}\) and a 99th-percentile error of \(9.9\times10^{-3}\,\mathrm{rad}\), accelerates the collision subroutine by 40\%, and reduces total wall time by 36\%. Finally, the same DeepONet--LJ scattering kernel is tested beyond viscosity-controlled flows through diffusion benchmarks.

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