A review and perspective on a convergence analysis of the direct simulation Monte Carlo and solution verification

In 1963, G. A. Bird published a research note on his investigation of a rigid sphere gas reaching translational equilibrium using a Monte Carlo type method. Since then, the method has been developed into a primary workhorse to computationally solve the Boltzmann kinetic equation. As it is increasingly applied to challenging problems in the real world, verification studies of the method have become a critical issue. In this paper, we review previous studies on this challenging subject and present a perspective on a convergence analysis of the direct simulation Monte Carlo (DSMC) method and solution verification. During this process, a verification method based on the physical laws of conservation is studied in depth. In particular, a convergence history plot on all three types of computational errors-decomposition, statistical, and round-off-is presented for two benchmark problems. Finally, future research topics to maximize the full potential of the DSMC method, pioneered by the late G. A. Bird, are suggested.