矩方法在动理学中的发展与应用  

The development and application of the moment method in the gas kinetic theory

作　　者：蔡振宁 樊玉伟[2] 胡志成[3] 李若[2] 王何宇[4] 

机构地区：[1]Department of Mathematics,Duke University,Durham,NC 27708,USA [2]北京大学数学科学学院、应用物理和技术研究中心,北京100871 [3]南京航空航天大学理学院数学系,南京211106 [4]浙江大学数学科学学院,杭州310027

出　　处：《中国科学：信息科学》2016年第10期1465-1488,共24页Scientia Sinica(Informationis)

基　　金：国家重点基础研究发展计划(973计划)(批准号:2011CB309704)资助项目

摘　　要：矩方法既是一种通过约简动理学方程获得宏观流体方程组的建模手段,又是求解动理学方程本身的数值方法,近年来发展迅速、应用广泛.本文从模型、数值方法和应用3个方面回顾和总结了动理学中矩方法的研究进展.首先讨论了矩方法的不足并总结了为弥补这些不足而提出的修正方法,特别是介绍了其中广为关注的正则化方法和全局双曲正则化矩方法;然后探讨了各种求解矩方法的数值方法,并重点介绍了针对于任意阶矩方程组的数值正则化方法.此外文章还回顾了矩方法在稀薄流体、微流、电子输运、等离子体和密度泛函等领域的应用,并展望了矩方法的进一步发展方向.The moment method is not only a modeling tool that gives macroscopic fluid equations by reducing kinetic equations,but also a numerical method for solving kinetic equations.It has been the subject of rapid development,and in recent years has acquired widespread applications.In this paper,we review and summarize the research development of moment methods in kinetic theory from the aspects of modeling,numerical methods,and applications.First,we discuss the deficiencies of moment methods and summarize the remedy,where in particular the regularized moment method and globally hyperbolic moment method are introduced,owing to the wide interest regarding them.Subsequently,we investigate various numerical methods for solving moment equations,and highlight the numerical regularized method for moment equations of arbitrary orders.In addition,this paper reviews the applications of moment methods in the fields of rarefied gases,microflows,electron transport,plasma,and density functionals and presents an outlook regarding the future development of moment methods.

关 键 词：气体动理学 矩方法 双曲性 正则化 模型约简 数值模拟 应用 

分 类 号：O241.8[理学—计算数学]