The molecular motion and collision processes are usually decoupled in the traditional molecular simulations, where the simulation process is divided into a series of time steps and the two processes are sequentially executed during each time step. The numerical errors in transport properties and flow-field solutions will become noticeable when the time step is much larger than the mean time interval between intermolecular collisions. The limitation of using small time step can be relaxed for multiscale problems by using coupled algorithm that allows the molecular motions and collisions to happen simultaneously. This coupling idea was proposed in the DSBGK method that however focused on the discussion of variance reduction. The same coupling idea has been also implemented in the recent USP-ESBGK method that focused on the advantage of using a coupled algorithm. As this is a significant advancement in particle simulation, we present the similarity analysis between the two methods in the coupling spirit as well as the difference in the detailed implementations.

在传统的分子模拟中，分子运动和碰撞过程通常是分离的，其中模拟过程分为一系列时间步长，两个过程在每个时间步长中依次执行。当时间步长比分子间碰撞之间的平均时间间隔大得多时，传输特性和流场解中的数值误差将变得明显。通过使用允许分子运动和碰撞同时发生的耦合算法，可以缓解多尺度问题对小时间步的限制。这种耦合思想是在DSBGK方法中提出的，但是重点在于方差减少的讨论。在最近的USP-ESBGK方法中也实现了相同的耦合思想，该方法集中于使用耦合算法的优势。由于这是粒子模拟的一项重大进步，因此，我们将结合耦合的精神介绍这两种方法之间的相似性，以及在具体实现上的差异。