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Despite fundamentally different implementations, both codes yield quantitatively identical results for key metrics, including linear and nonlinear growth rates, mode structures, nonlinear saturation levels, Poincaré plots, and scaling laws. The findings indicate that outcomes depend on equilibrium and boundary conditions rather than code implementation or initial perturbations.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/nonlinear-benchmarking-between-clt-and-m3d-c1-a-study-of-tearing-and-resistive-kink-modes/268785/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/nonlinear-benchmarking-between-clt-and-m3d-c1-a-study-of-tearing-and-resistive-kink-modes/268785.png","ImageObject",300,407,{"name":42,"@type":43},"Tawan","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-27","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",11,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What instabilities are compared in the benchmarking between CLT and M3D-C1?","Question",{"text":63,"@type":64},"The paper benchmarks the nonlinear tearing mode and the resistive-kink mode between the CLT and M3D-C1 codes.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do CLT and M3D-C1 differ in numerical implementation?",{"text":68,"@type":64},"CLT is an explicit finite-difference code, while M3D-C1 is an implicit finite-element code.",{"name":70,"@type":61,"acceptedAnswer":71},"What common result does the benchmarking claim about the simulation outputs?",{"text":72,"@type":64},"It reports that linear and nonlinear growth rates, mode structures, nonlinear saturation levels, Poincaré plots, and scaling laws are quantitatively the same, implying dependence mainly on equilibrium and boundary conditions.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},268785,1789436874,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":99,"preview_page_count":4},2336475104042,"https://ap-avatar.wpscdn.com/avatar/22000c4c32af1715be0?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786537525561427321","Nonlinear benchmarking between CLT and M3D-C1  \nW. Zhang 1, S. C. Jardin2 , Z. W. Ma 1,a), A. Kleiner2, and H. W. Zhang 1  \n1Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, Hangzhou 310027, China  \n2Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543, USA  \nAbstract: A systematical benchmarking between the CLT code and the M3D-C1 code is presented, including the nonlinear tearing mode and resistive-kink mode. CLT is an explicit finite difference code, while M3D-C1 is an implicit finite element code. Although the implementations of CLT and M3D-C1 are totally different, we find that the simulation results of the resistive-kink mode and the m/n=2/1 tearing mode from M3D-C1 and CLT are quantitatively the same, including the linear and nonlinear growth rates, the mode structures, the nonlinear saturation levels, the Poincare plots, and the scaling laws. This confirms that the simulation results of the MHD instabilities are only determined by the equilibrium and boundary conditions, and are independent of the code implementations and the initial perturbations. This, in turn, implies that the nonlinear results of the two codes are correct and accurate.  \na) Corresponding Author: [zwma@zju.edu.cn](zwma@zju.edu.cn)  \nI. Introduction  \nTearing modes are common phenomena in tokamaks. The tearing modes are the primary cause of the degradation oftokamak performance[1] and even disruptions.[2] Sawteeth, which not only flatten the plasma temperature but also may trigger neo-classical tearing modes in nearby resonant surfaces,[3, 4] are believed to be related to the nonlinear evolution of the resistive-kink mode. [5, 6] It is worthwhile to investigate these instabilities to increase our understanding with the goal of achieving high-performance operation in future fusion reactors.[7, 8]  \nThe resistive tearing mode was first studied by Furth et al., who found that the linear growth rate scales as γ ~ S −3/5 , where S is the Lundquist number. [9] The first analytical theory of the resistive-kink mode was that by by Coppi et al. [6], who found that the linear growth rate scales as γ ~ S −1/3 . Not only linear studies but also nonlinear theoretical studies have been reported in the past decades.[10-12] It should be noted that significant simplification of the physical model and the geometry is applied in these theoretical analytical studies. To confirm that these assumptions are reasonable and to gain more insight into those instabilities, simulation studies have been widely conducted. [13, 14] Since the implementation of different codes are different,[15-19] and the nonlinear evolution from different simulation codes sometimes are significantly different, it is difficult to say which simulations are correct.  \nOne way to verify the simulation results is to quantitatively benchmark between different codes. This method can be effective, but it is still a challenge since the nonlinear simulation results can be sensitive to many details of the formulation, the equilibrium, the boundary conditions and the initial conditions. The M3D-C1 code isan implicit, three-dimensional high-order finite-element code for the solution of the time-dependent linear or nonlinear two-fluid magnetohydrodynamic (MHD) equations in cylindrical or toroidal geometry. [17] The CLT code is an explicit three-dimensional finite-difference nonlinear MHD code for toroidal geometry. [19] Although they are both used to investigate MHD instabilities in tokamaks, the  \nimplementations in the two codes are totally different. Quantitative benchmarking the two codes on several problems could demonstrate that the simulation results of both codes are accurate. In the present paper, the benchmarking between CLT and M3D-C1, including the linear and nonlinear evolution of the tearing modes and the resistive-kink mode, is presented.  \nII. Model descriptions, normalizations, and code implementations.  \nBefore the benchmarking be","cbCaiotMpS357Gnq","https://ap.wps.com/l/cbCaiotMpS357Gnq","pdf",2280659,24,"English","# I. Introduction\n# II. Model descriptions, normalizations, and code implementations","[{\"question\":\"What instabilities are compared in the benchmarking between CLT and M3D-C1?\",\"answer\":\"The paper benchmarks the nonlinear tearing mode and the resistive-kink mode between the CLT and M3D-C1 codes.\"},{\"question\":\"How do CLT and M3D-C1 differ in numerical implementation?\",\"answer\":\"CLT is an explicit finite-difference code, while M3D-C1 is an implicit finite-element code.\"},{\"question\":\"What common result does the benchmarking claim about the simulation outputs?\",\"answer\":\"It reports that linear and nonlinear growth rates, mode structures, nonlinear saturation levels, Poincaré plots, and scaling laws are quantitatively the same, implying dependence mainly on equilibrium and boundary conditions.\"}]","Nonlinear Benchmarking between CLT and M3D-C1 - A Study of Tearing and Resistive-Kink Modes | PDF"]