近年来，新型高超声速飞行器不断涌现，飞行高度突破了传统航空领域的范围，空天一体化趋势明显。跨流域飞行带来的稀薄气体效应不可忽略，对于这类多尺度流场的模拟和气动特性分析，单一尺度的计算方法，如基于NS方程的计算流体力学（CFD）和基于分子的直接模拟蒙特卡洛（DSMC）方法，均不能同时满足精度和效率的要求。课题组与合作者发展了耦合分子运动和碰撞的统一随机粒子（USP）方法[1, 2]，如图1所示，突破了传统粒子方法的时空步长限制，将粒子方法在近连续流域的计算效率提高了几个数量级，并发布了基于USP方法的开源求解器SPARTACUS[3]，可高效模拟三维高超声速跨流域流动, 如图2所示。我们已应用SPARTACUS软件成功模拟了多种高速气体流动，包括多原子气体分子的内能激发等效应[4]。

近期，我们将以上多尺度计算思想拓展到了Fokker-Planck模型，发展了多尺度随机粒子（MSP）方法，同样具有时空二阶精度[5]。同时，我们采用USP方法对可压缩衰减各向同性湍流开展了多尺度模拟，阐明了分子热涨落对湍流谱和湍流可预测性的影响[6]。

Fig. 1. Comparison of DSMC and USP methods.

Fig. 2. The application of SPARTACUS to hypersonic flows.

[1] F. Fei, J. Zhang*, J. Li, and Z. H. Liu*, "A unified stochastic particle Bhatnagar-Gross-Krook method for multiscale gas flows," Journal of Computational Physics 400, 108972 (2020).

[2] K. Feng, Z. Cui, P. Tian, and J. Zhang^*, "A unified stochastic particle method with spatiotemporal adaptation for simulating multiscale gas flows," Journal of Computational Physics 505, 112915 (2024).

[3] K. Feng, P. Tian, J. Zhang*, F. Fei, and D. Wen, "SPARTACUS: An open-source unified stochastic particle solver for the simulation of multiscale nonequilibrium gas flows," Comput. Phys. Commun. 108607 (2023).

[4] P. Tian, K. Feng, Q. Ma, Z. Li, J. Zhang*, "Unified stochastic particle simulation of polyatomic gas flows using SPARTACUS," Computers & Fluids 265, 105987 (2023).

[5] Z. Cui, K. Feng, Q. Ma, and J. Zhang*, "A multiscale stochastic particle method based on the Fokker-Planck model for nonequilibrium gas flows," Journal of Computational Physics 520, 113458 (2025).

[6] Q. Ma, C. Yang, S. Chen, K. Feng, Z. Cui, and J. Zhang*, "Effect of thermal fluctuations on spectra and predictability in compressible decaying isotropic turbulence," Journal of Fluid Mechanics 987, A29 (2024).