标题： Crank-Nicolson BGK 积分器用于多尺度基于粒子的动理学模拟 显示英文标题

标题： Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations

摘要： 求解Bhatnagar-Gross-Krook（BGK）方程的随机粒子方法能够高效且灵活地模拟介于连续介质流和自由分子流之间的过渡区流动。 然而，通常在粒子运动和松弛之间进行的一阶算子分裂会对时间步长造成限制，导致计算成本随着气体密度的增加而增加。 在此引入了Crank-Nicolson随机粒子BGK（CN-SPBGK）方法，作为一种先进的基于粒子的动理学求解器，专为多尺度气体流动模拟设计。 该方法在所有Knudsen数范围内以二阶精度整合BGK方程，而无需额外参数，同时在连续介质区域渐近保持Navier-Stokes通量。 在多个测试案例中与现有粒子BGK方法进行了比较，CN-SPBGK表现出更一致的收敛性和准确性。 显示英文摘要

摘要： Solving the Bhatnagar-Gross-Krook (BGK) equation with a stochastic particle approach enables efficient and flexible simulations of flows in the transition regime, between continuum and free molecular flow. However, the usual first-order operator splitting between particle movement and relaxation imposes restrictions on the time step, causing the computational cost to increase with the gas density. The Crank-Nicolson stochastic particle BGK (CN-SPBGK) method is introduced here as an advanced particle-based kinetic solver designed for multi-scale gas flow simulations. This method integrates the BGK equation with second-order accuracy across all Knudsen number regimes without requiring additional parameters, while asymptotically preserving the Navier-Stokes flux in the continuum regime. Comparisons with pre-existing particle BGK methods are conducted on several test cases, with CN-SPBGK demonstrating more consistent convergence and accuracy.