Shterev Kiril
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bontchev St., bl. 4, 1113 Sofia, Bulgaria.
Micromachines (Basel). 2021 Jan 26;12(2):127. doi: 10.3390/mi12020127.
Micro-electromechanical systems (MEMS) have developed rapidly in recent years in various technical fields that have increased their interest in the Direct Simulation Monte Carlo (DSMC) method. In this paper, we present a simple representation of the DSMC collision scheme and investigate the correctness of the Simplified Bernoulli Trial (SBT) collision scheme for the calculation of two-dimensional flows. The first part of the collision scheme, which determines collision pairs, is presented following the derivation of the expression for the mean free path and using the cumulative distribution function. Approaches and conclusions based on one-dimensional flows are not always directly applicable to two- and three-dimensional flows. We investigated SBT correctness by using the two-dimensional pressure-driven gas flow of monoatomic gas as a test case. We studied the influence of shuffling of the list of particles per cell (PPC) before the collision scheme's execution, as well as the minimal and maximal number of PPC, on the correctness of the solution. The investigation showed that shuffling and the number of PPC played an important role in the correctness of SBT. Our recommendations are straightforwardly applicable to three-dimensional flows. Finally, we considered the mixing of two gases and compared the results available in the literature.
近年来，微机电系统（MEMS）在各个技术领域发展迅速，这些领域对直接模拟蒙特卡罗（DSMC）方法的兴趣也与日俱增。在本文中，我们给出了DSMC碰撞方案的一种简单表示，并研究了简化伯努利试验（SBT）碰撞方案用于二维流动计算的正确性。碰撞方案的第一部分用于确定碰撞对，它是在推导平均自由程表达式并使用累积分布函数之后给出的。基于一维流动的方法和结论并不总是直接适用于二维和三维流动。我们以单原子气体的二维压力驱动气流为测试案例，研究了SBT的正确性。我们研究了在碰撞方案执行之前每个单元格中粒子列表（PPC）的洗牌操作以及PPC的最小和最大数量对解的正确性的影响。研究表明，洗牌操作和PPC的数量对SBT的正确性起着重要作用。我们的建议可直接应用于三维流动。最后，我们考虑了两种气体的混合，并比较了文献中的现有结果。
