A New Implementation of a Fourth-Order CESE Scheme for 3D MHD Simulations

A New Implementation of a Fourth-Order CESE Scheme for 3D MHD Simulations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A New Implementation of a Fourth-Order CESE Scheme for 3D MHD Simulations Chaowei Jiang, Ling Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4961971/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Mar, 2025 Read the published version in Solar Physics → Version 1 posted 7 You are reading this latest preprint version Abstract This paper is devoted to the description and validation of a new implementation of a fourth-order space-time conservation-element and solution-element (CESE) scheme to numerically solve the time-dependent, three-dimensional (3D) magnetohydrodynamic (MHD) equations. The core of the scheme is that, with the aid of a grid staggered in space and time, the conservative variables are advanced by integration of the controlling equation in the space-time four-dimensional domain by utilizing Taylor expansion, and their spatial derivatives are computed by finite difference with $p$ order derivatives from $p-1$ order ones. The new scheme achieves fourth-order accuracy in both space and time simultaneously, using a compact stencil identical to that in the second-order CESE scheme. We provide a general framework for convenience of programming such that the scheme can be easily extended to arbitrarily higher order by including higher-order terms in the Taylor series. A suite of 3D MHD tests demonstrate that the fourth-order CESE scheme at relatively low grid resolutions can obtain reliable solution comparable to the second-order CESE scheme at four-times high resolution, and showing a very high efficiency in computing by using only around $5%$ of the computing resources. Space-time conservation-element and solution-element (CESE) method Magnetohydrodynamics (MHD) Computational fluid dynamics (CFD) High-order scheme Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 28 Mar, 2025 Read the published version in Solar Physics → Version 1 posted Editorial decision: Revision requested 09 Jan, 2025 Reviews received at journal 08 Jan, 2025 Reviewers agreed at journal 01 Jan, 2025 Reviewers invited by journal 30 Aug, 2024 Editor assigned by journal 24 Aug, 2024 Submission checks completed at journal 24 Aug, 2024 First submitted to journal 23 Aug, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4961971","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":352240433,"identity":"8fc9e5ee-3534-4ecb-908f-b70485b1397e","order_by":0,"name":"Chaowei Jiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYDACCQgpZ8AMotlI0GJswMxMmhaGxA0MxGrhn9388DFPhUX6dnb+Awwfyg4DRRoIWHLnmLExzxmJ3J3NzAyMM84dBoocwK/FQCLBTDq3TSJ3w2FmBmbetsMgEUJa0r9J5/6TSDcAaflLnJYcoC0NEglgLYzEaJG4kVNs/OeYhCHQYQYHe86l80jcIKCFf0b6xoczaurkDc4ffPjgR5m1HP8MAlpQwAEg5iFB/SgYBaNgFIwCXAAATUw7snDJZjIAAAAASUVORK5CYII=","orcid":"","institution":"Harbin Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Chaowei","middleName":"","lastName":"Jiang","suffix":""},{"id":352240434,"identity":"85b494e1-3c85-442b-ae3b-ab76e938df7f","order_by":1,"name":"Ling Zhang","email":"","orcid":"","institution":"Harbin Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Ling","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-08-23 06:35:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4961971/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4961971/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11207-025-02452-w","type":"published","date":"2025-03-28T15:57:16+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":79604842,"identity":"6d000142-a0c0-438f-8b44-2bce359b9a49","added_by":"auto","created_at":"2025-03-31 16:07:31","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1908637,"visible":true,"origin":"","legend":"","description":"","filename":"solaexample6.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4961971/v1_covered_87a65943-8397-4503-b633-b1fbff60f1c1.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A New Implementation of a Fourth-Order CESE Scheme for 3D MHD Simulations","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"solar-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sola","sideBox":"Learn more about [Solar Physics](http://link.springer.com/journal/11207)","snPcode":"11207","submissionUrl":"https://submission.nature.com/new-submission/11207/3","title":"Solar Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Space-time conservation-element and solution-element (CESE) method, Magnetohydrodynamics (MHD), Computational fluid dynamics (CFD), High-order scheme","lastPublishedDoi":"10.21203/rs.3.rs-4961971/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4961971/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" This paper is devoted to the description and validation of a new implementation of a fourth-order space-time conservation-element and solution-element (CESE) scheme to numerically solve the time-dependent, three-dimensional (3D) magnetohydrodynamic (MHD) equations. 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