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Study on a Gridless Solver for Micro-Scale Flows based on the Boltzmann Equation

基于Boltzmann方程的微尺度流动无网格求解器研究

基本信息

批准号：
15560140
负责人：
MORINISHI Koji
金额：
$ 2.11万
依托单位：
Kyoto Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

In this study, a novel simulation method based on the Boltzmann equation has been developed for gas flows in micro scales. Numerical simulation for gas flows about micro devices is one of the recent new frontiers of computational fluid dynamics(CFD). It can be an essential tool for understanding the fluid behavior around Micro-Electro-Mechanical Systems(MEMS) and Nano Technology Base Systems(NTBS). Since the Knudsen numbers, the ratio of molecular mean free path to a characteristic flow length, of the flows around MENS and NTBS are typically between 0.01 and 10, simulation method based on the Boltzmann (kinetic) approach should be preferable. One of the numerical methods widely used for the Boltzmann equation is the direct simulation Monte Carlo(DSMC) method. The DSMC method is a powerful simulation tool for supersonic rarefied gas flows. The method, however, becomes a poor simulation tool for the flows in micro scales, because the micro-scale flows are low speed flows, for which huge sample size is required to reduce the inherent statistical scatter of the DSMC method. In contrast with it, the novel simulation method for the Boltzmann equation does not have any statistical scatter in the solution. The third order upwind gridless method is used for estimating the convective terms of the equation. The collision integral is approximated with a kinetic model collision term, which correctly resembles the lower 13 moments of the Boltzmann equation. The simulation method is as powerful as the DSMC method for supersonic flows and definitely superior to the DSMC method for subsonic flows. The simulation method can predict micro-scale low speed flows and is also superior to the IP(Information Preservation) method, which is a novel statistical method developed for low speed rarefied gas flows.

在这项研究中，一种新的模拟方法的基础上玻尔兹曼方程已被开发的气体流动在微尺度。微器件周围气体流动的数值模拟是计算流体力学（CFD）研究的新前沿之一。它可以成为理解微机电系统（MEMS）和纳米技术基础系统（NTBS）周围流体行为的重要工具。由于克努森数，分子平均自由程的特征流动长度的比率，在MENS和NTBS周围的流动通常是在0.01和10之间，基于玻尔兹曼（动力学）方法的模拟方法应该是优选的。Boltzmann方程的一种广泛使用的数值方法是直接模拟Monte Carlo（DSMC）方法。DSMC方法是研究超音速稀薄气体流动的有力工具。然而，该方法成为一个穷人的模拟工具，在微尺度流动，因为微尺度流动是低速流动，这需要大量的样本量，以减少固有的统计离散的DSMC方法。与之相比，Boltzmann方程的新模拟方法在解中没有任何统计散射。采用三阶迎风无网格方法对方程的对流项进行了数值计算。碰撞积分近似的动力学模型碰撞项，这正确地类似于较低的13个时刻的玻尔兹曼方程。对于超音速流动，该模拟方法与DSMC方法一样强大，而对于亚音速流动，该方法明显优于DSMC方法上级。该方法能较好地预测微尺度低速流动，且优于针对低速稀薄气体流动发展起来的一种新的统计方法IP（Information Preservation）方法。