Coupling the molecular motion and collision processes in numerical simulations

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.