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

• Published in: Physics of fluids (1994) Vol. 31; no. 6
• Main Authors: Karchani, A., Ejtehadi, O.
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.06.2019
• Subjects: Computer simulation; Convergence; Direct simulation Monte Carlo method; Fluid dynamics; Kinetic equations; Physics
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5093746

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.