SCELT (symbolic computation aided eigenvalue and linear code for tokamaks): A full MHD eigenvalue code in toroidal geometry developed with the use of a symbolic computation technique

doi:10.1016/j.cpc.2022.108412

	SCELT (symbolic computation aided eigenvalue and linear code for tokamaks): A full MHD eigenvalue code in toroidal geometry developed with the use of a symbolic computation technique
	Ma, J.; Guo, W.
刊名	COMPUTER PHYSICS COMMUNICATIONS
	2022-09-01
卷号	278
关键词	Full MHD Symbolic computation technique Eigenvalue Vector analysis Automatic numerical discretization Toroidal geometry
ISSN号	0010-4655
DOI	10.1016/j.cpc.2022.108412
通讯作者	Guo, W.(wfguo@ipp.ac.cn)
英文摘要	In this work, we report the construction of an eigenvalue computer code largely in C++ language, SCELT, by using the symbolic computation technique for the first time to solve the linearized single fluid magnetohydrodynamic (MHD) eigenvalue problem in toroidal geometry. A symbolic vector analysis module is developed to function the automatic derivation of the tedious linearized full MHD equations in the magnetic flux coordinate system. Furthermore, another module is developed to implement the automatic numerical discretization. These two modules dramatically reduce the human workload and obviate the possibility of a mistake during code development. The tools provide a means of constructing matrices from differential operations and can be used for (generalized) linear problems, such as source driven and eigenvalue problems. Demo uses of both the symbolic vector analysis module and automatic numerical discretization module, such as the Poisson equation and tokamak equilibrium equation, are presented to demonstrate their advantages and potential broad applications. The full MHD eigenvalue code developed with these two modules is verified by the internal kink mode and tearing mode tests. Program summary Program Title: SCELT (Symbolic Computation aided Eigenvalue and Linear code for Tokamaks) CPC Library link to program files: https://doi .org /10 .17632 /35h3xmc28k.1 Licensing provisions: GNU General Public License 3.0 Programming language: C++, MATLAB External routines/libraries: center dot EIGEN (https://eigen .tuxfamily.org /index .php ?title =Main _Page) Nature of problem: The eigenvalue full MHD model determines a wide range of physical phenomena arising from the basic destabilizing forces, which are of considerable both fundamental and practical importance for magnetic fusion plasmas. From the viewpoint of physics, solving the model is equivalent to finding the spectrum of the system, and for realistic tokamak geometry, it becomes possible only with the help of computer simulation. From the viewpoint of mathematics, it is actually a problem of solving a set of partial differential equations in a general curvilinear coordinate system. Solution method: Different from the conventional method, a symbolic vector analysis module using the symbolic computation technique is developed to conduct the automatic expansion of the full MHD equations in the magnetic flux coordinate system. In addition, an automatic numerical discretization module is developed to automatically implement the numerical discretization. Facilitated by the two modules, the coefficients of the matrices of the eigenvalue equation will be automatically generated and passed to the linear eigenvalue solver (eig function of MATLAB). The eigenvalues and eigenvectors are resolved by the solver. Additional comments including restrictions and unusual features: As originally motivated by the development of an eigenvalue full MHD code, a symbolic vector analysis module by using symbolic computation technique and a closely related automatic numerical discretization module are developed and directly applied to physics code development for the first time at least in the fusion field. Many (generalized) linear physics problems can benefit from the standalone or integrated application of these two modules. The tokamak equilibrium and eigenvalue MHD problems presented in the paper can be considered two important and practical examples. (c) 2022 Published by Elsevier B.V.
资助项目	National Key R&D Program of China[2017YFE0300402] ; National Natural Science Foundation of China[12075282] ; National Natural Science Foundation of China[11775268]
WOS关键词	INTERNAL KINK MODES ; STABILITY CODE ; IDEAL ; PLASMAS
WOS研究方向	Computer Science ; Physics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000806796400001
资助机构	National Key R&D Program of China ; National Natural Science Foundation of China
内容类型	期刊论文
源URL	[http://ir.hfcas.ac.cn:8080/handle/334002/131165]
专题	中国科学院合肥物质科学研究院
通讯作者	Guo, W.
作者单位	Chinese Acad Sci, Inst Plasma Phys, Hefei 230031, Peoples R China
推荐引用方式 GB/T 7714	Ma, J.,Guo, W.. SCELT (symbolic computation aided eigenvalue and linear code for tokamaks): A full MHD eigenvalue code in toroidal geometry developed with the use of a symbolic computation technique[J]. COMPUTER PHYSICS COMMUNICATIONS,2022,278.
APA	Ma, J.,&Guo, W..(2022).SCELT (symbolic computation aided eigenvalue and linear code for tokamaks): A full MHD eigenvalue code in toroidal geometry developed with the use of a symbolic computation technique.COMPUTER PHYSICS COMMUNICATIONS,278.
MLA	Ma, J.,et al."SCELT (symbolic computation aided eigenvalue and linear code for tokamaks): A full MHD eigenvalue code in toroidal geometry developed with the use of a symbolic computation technique".COMPUTER PHYSICS COMMUNICATIONS 278(2022).