数值李变换方法及Vlasov系统的非线性数值模拟研究
发布时间：2018-12-20 15:53
【摘要】：湍流输运是磁约束等离子体研究的重要课题之一。准线性理论很好地预言了一些情况下系统的输运。然而在更多的非线性情况下,由湍流导致的系统输运,在理论上仍然很难处理。随着计算机技术的发展,数值模拟已经在等离子体湍流输运研究中扮演着越来越重要的角色。本文首先介绍了基于全新的数值李变换方法所开发一维无碰撞Vlasov系统的模拟程序。新的程序以I-变换理论为基础,数值上结合了连续性方法以及特征线方法,即避免了粒子模拟存在较大系统噪声的问题,又兼具了特征线方法较强的数值稳定性的特点,在模拟中能采用比较长的时间步长。计算中,我们利用多步变换的方法,在数值上完美地解决了微扰方法在粒子俘获问题上固有的困难,使得程序能够准确地模拟系统线性阶段以及非线性阶段的演化。在一维Landau阻尼问题以及双峰不稳定性问题的算例中,新程序的计算结果与传统方法得到的结果一致。然后我们利用新程序分析了随机电场扰动问题以及双峰不稳定性问题中粒子在速度空间的输运。相较于传统的模拟方法,新的基于微扰理论的模拟方法其中间变量与输运系数有着直接的关联,在数值计算中能够方便地得到系统的输运系数。模拟的结果显示,在系统受到随机场扰动和线性阶段的湍流扰动时,利用新的模拟方法得到的输运系数与实际的结果吻合。而在湍流的非线性阶段,由于大尺度结构的存在,新方法以及准线性方法所计算得到的输运系数与实际的结果有了较大的偏差。接着我们利用数值李变换程序计算了一维无碰撞系统演化过程中的熵产生。与传统数值上用于计算熵的公式不同,我们采用了理论上广为接受的利用粗网平均分布函数来计算系统熵产生的方法。在随机扰动场算例,线性Landau阻尼算例和双峰不稳定性算例中,我们发现随着粗网平均长度的增加,计算所得的熵产生是收敛的,并且当分布函数与麦克斯韦分布接近时,我们计算所得到的熵产生,与热力学定义的熵产生是一致的。我们还讨论了上述情况中粗网平均长度的选取对计算所得熵产生的影响以及非麦克斯韦分布对熵计算的影响。最后,讨论了基于数值李变换方法发展的环位形非线性回旋动理学模拟程序NLT非线性调试中的守恒性问题和滤波问题的处理方法。
[Abstract]:Turbulent transport is one of the most important topics in the study of magnetically confined plasma. The quasilinear theory well predicts the transport of the system in some cases. However, in more nonlinear cases, the system transport caused by turbulence is still difficult to deal with theoretically. With the development of computer technology, numerical simulation has played a more and more important role in the study of plasma turbulence transport. This paper first introduces the simulation program of one-dimensional collision-free Vlasov system based on the new numerical lie transform method. The new program is based on the I- transformation theory and combines the continuity method and the feature line method numerically, which avoids the problem of large system noise in particle simulation and has the characteristics of strong numerical stability of the feature line method. A longer time step can be used in the simulation. In the computation, we use the multi-step transformation method to solve the inherent difficulty of the perturbation method in the particle capture problem numerically, so that the program can accurately simulate the evolution of the linear and nonlinear stages of the system. In the case of one-dimensional Landau damping problem and bimodal instability problem, the results obtained by the new program are in agreement with those obtained by the traditional method. Then we use the new program to analyze the particle transport in the velocity space in the stochastic electric field perturbation problem and the bimodal instability problem. Compared with the traditional simulation method, the new simulation method based on perturbation theory has a direct correlation between the intermediate variables and the transport coefficient, and the transport coefficient of the system can be easily obtained in the numerical calculation. The simulation results show that the transport coefficients obtained by the new simulation method are in good agreement with the actual results when the system is subjected to random field disturbances and linear turbulence disturbances. However, in the nonlinear stage of turbulence, due to the existence of large-scale structures, the transport coefficients calculated by the new method and the quasi-linear method are quite different from the actual results. Then we use the numerical lie transform program to calculate the entropy generation in the evolution of one dimensional collision-free systems. Different from the traditional formula used to calculate entropy, we adopt the widely accepted method of calculating the entropy of the system by using the mean distribution function of rough net. In the examples of random disturbance field, linear Landau damping and bimodal instability, we find that the entropy generation is convergent with the increase of average length of rough net, and when the distribution function is close to Maxwell distribution, The entropy generated by our calculations is consistent with the entropy generation defined by thermodynamics. We also discuss the influence of the average length of the rough net on the calculated entropy and the influence of the non-Maxwell distribution on the entropy calculation. Finally, the conservation and filtering problems in NLT nonlinear cyclotron simulation program based on the numerical lie transform method are discussed.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O53
本文编号：2388207
[Abstract]:Turbulent transport is one of the most important topics in the study of magnetically confined plasma. The quasilinear theory well predicts the transport of the system in some cases. However, in more nonlinear cases, the system transport caused by turbulence is still difficult to deal with theoretically. With the development of computer technology, numerical simulation has played a more and more important role in the study of plasma turbulence transport. This paper first introduces the simulation program of one-dimensional collision-free Vlasov system based on the new numerical lie transform method. The new program is based on the I- transformation theory and combines the continuity method and the feature line method numerically, which avoids the problem of large system noise in particle simulation and has the characteristics of strong numerical stability of the feature line method. A longer time step can be used in the simulation. In the computation, we use the multi-step transformation method to solve the inherent difficulty of the perturbation method in the particle capture problem numerically, so that the program can accurately simulate the evolution of the linear and nonlinear stages of the system. In the case of one-dimensional Landau damping problem and bimodal instability problem, the results obtained by the new program are in agreement with those obtained by the traditional method. Then we use the new program to analyze the particle transport in the velocity space in the stochastic electric field perturbation problem and the bimodal instability problem. Compared with the traditional simulation method, the new simulation method based on perturbation theory has a direct correlation between the intermediate variables and the transport coefficient, and the transport coefficient of the system can be easily obtained in the numerical calculation. The simulation results show that the transport coefficients obtained by the new simulation method are in good agreement with the actual results when the system is subjected to random field disturbances and linear turbulence disturbances. However, in the nonlinear stage of turbulence, due to the existence of large-scale structures, the transport coefficients calculated by the new method and the quasi-linear method are quite different from the actual results. Then we use the numerical lie transform program to calculate the entropy generation in the evolution of one dimensional collision-free systems. Different from the traditional formula used to calculate entropy, we adopt the widely accepted method of calculating the entropy of the system by using the mean distribution function of rough net. In the examples of random disturbance field, linear Landau damping and bimodal instability, we find that the entropy generation is convergent with the increase of average length of rough net, and when the distribution function is close to Maxwell distribution, The entropy generated by our calculations is consistent with the entropy generation defined by thermodynamics. We also discuss the influence of the average length of the rough net on the calculated entropy and the influence of the non-Maxwell distribution on the entropy calculation. Finally, the conservation and filtering problems in NLT nonlinear cyclotron simulation program based on the numerical lie transform method are discussed.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O53
【相似文献】
相关期刊论文 前10条
1 张钧强;;关于全变换方法的研究和探讨[J];科技信息(科学教研);2008年09期
2 高婷婷;张明会;;分割变换方法在数学分析中的应用[J];首都师范大学学报(自然科学版);2013年05期
3 王国荣;简逢敏;;直接解算误差或条件方程组的平面映象变换方法[J];勘察技术;1978年02期
4 胡友秋;轴对称磁静平衡态Ⅰ.微变换方法[J];空间科学学报;1988年04期
5 刘林;;非正则形式变换方法的应用[J];南京大学学报(自然科学版);1983年02期
6 陈宇，王遵立，王瑞光，，朴燕;一种布尔变换及解变换方法在数据处理中的应用[J];发光学报;1996年03期
7 陈永衡;耦合振荡规律的数学描述[J];烟台师范学院学报(自然科学版);1998年03期
8 刘林;;关于非线性系统变换方法的几点注解[J];天文学报;1982年03期
9 姚海敏;赵一晗;;自由网参考基准变换方法的探讨[J];铁道勘察;2006年06期
10 刘林,章圣泮;非正则形式的变换方法及其应用[J];中国科学(A辑 数学 物理学 天文学 技术科学);1983年05期
相关会议论文 前2条
1 刘丽华;肜淼;刘扬;商德江;;半空间全息变换方法反演材料反射系数[A];中国声学学会2006年全国声学学术会议论文集[C];2006年
2 暴雪梅;何祚镛;;宽带、非共形全息声场变换方法[A];水下噪声学术论文选集（1985-2005）[C];2005年
相关博士学位论文 前2条
1 陈特欢;管线流动最优控制计算研究[D];浙江大学;2016年
2 戴宗良;数值李变换方法及Vlasov系统的非线性数值模拟研究[D];中国科学技术大学;2017年
相关硕士学位论文 前3条
1 李小英;基于Java的逆向变换方法及工具的研究[D];汕头大学;2002年
2 周甄川;一个3×3矩阵谱问题及其Darboux变换[D];华东师范大学;2006年
3 向朝森;基于二值形态学的形态变换方法及应用[D];中南民族大学;2011年
本文编号：2388207
本文链接：https://www.wllwen.com/shoufeilunwen/jckxbs/2388207.html
