中国电机工程学报2016，Vol.36Issue(4)：1148-1155,1200,9.DOI:10.13334/j.0258-8013.pcsee.2016.04.030
基于改进的多项近似法解玻尔兹曼方程计算电子输运系数
Computation of Electron Transport Coefficients Based on Improved Multi-term Approximation of the Boltzmann Equation
摘要
Abstract
The propagation properties of streamer could be obtained accurately by using the fluid model to simulate, provided that precise electron transport and reaction coefficients were input the model. Presently, there were two methods to calculate the transport coefficients: interpolation method based on the data of swarm experiment or two-term approximation of the Boltzmann equation. It was showed that interpolation method could be merely used in low reduced electric condition, and for the second method the reasonableness of the isotropic assumption and the accuracy of the results were a question. In view of the above problems, multi-term approximation of the Boltzmann equation to obtain electron transport coefficients was proposed by Nesset al. Here two improvements are provided: firstly, the expansion sequence is adjusted to derive the unified hierarchy in the hydrodynamic and non-hydrodynamic limit; secondly, the collision integral is evaluated based on the Gauss-Kronrod rule instead of Gauss-Laguerre rule as used in Ness''s works. In the end hard sphere model and Reid''s ramp inelastic model are considered. It is shown that it is more accurate to evaluate the collision integral based on Gauss-Kronrod integration method than Gauss-Laguerre method. Furthermore, it is demonstrated that the electron velocity distribution is anisotropic even only undergoing conservative collision, so there is a great error if the two -term approximation is used to obtain the electron transport coefficients.关键词
流体模型/玻尔兹曼方程/多项近似/各向异性/碰撞算子/Burnett多项式/球梯度算子Key words
fluid model/Boltzmann equation/multi-term approximation/anisotropic/collision operator/Burnett polynomial/spherical gradient operator分类
信息技术与安全科学引用本文复制引用
蔡新景,王新新,邹晓兵,鲁志伟..基于改进的多项近似法解玻尔兹曼方程计算电子输运系数[J].中国电机工程学报,2016,36(4):1148-1155,1200,9.基金项目
国家自然科学基金项目(51207019).The National Natural Science Foundation of China (51207019). （51207019）
