Efficient Cell-centered Nodal Integral Method for Multi-dimensional Burgers’ Equations

Efficient Cell-centered Nodal Integral Method for Multi-dimensional Burgers’ Equations | 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 Efficient Cell-centered Nodal Integral Method for Multi-dimensional Burgers’ Equations Nadeem Ahmed, Ram Prakash Bharti, Suneet Singh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5780462/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 22 Jul, 2025 Read the published version in Engineering with Computers → Version 1 posted 9 You are reading this latest preprint version Abstract An efficient coarse-mesh nodal integral method (NIM), based on cell-centered variables and referred to as cell-centered NIM (CCNIM), is developed and applied for solving multi-dimensional, time-dependent, Burgers’ equations. Unlike traditional NIM, which utilizes surface-averaged variables as discrete unknowns, this innovative approach formulates the final expression of the numerical scheme using discrete unknowns represented by cell-centered or node-averaged variables. By relying on these cell centroids, the proposed CCNIM approach presents several advantages compared to traditional NIM. These include a simplified implementation process in terms of local coordinate systems, enhanced flexibility regarding the higher order of accuracy in time, straightforward formulation for higher-degree temporal derivatives, and offering a viable option for coupling with other physics. The multidimensional time-dependent Burgers’ problems with known analytical solutions are solved in order to validate the developed scheme. Furthermore, a detailed comparison between the proposed CCNIM approach and other traditional NIM schemes is conducted to showcase its effectiveness. The simplicity and robustness of the approach provide a strong foundation for its seamless extension to more complex fluid flow problems. Burgers’ equations Difference equations Analytical nodal methods Coarse-mesh methods Cell-centered nodal integral method Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 22 Jul, 2025 Read the published version in Engineering with Computers → Version 1 posted Editorial decision: Revision requested 18 Feb, 2025 Reviews received at journal 14 Feb, 2025 Reviews received at journal 12 Feb, 2025 Reviewers agreed at journal 17 Jan, 2025 Reviewers agreed at journal 17 Jan, 2025 Reviewers invited by journal 15 Jan, 2025 Editor assigned by journal 07 Jan, 2025 Submission checks completed at journal 07 Jan, 2025 First submitted to journal 07 Jan, 2025 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-5780462","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":399140339,"identity":"9cf661b1-028a-4680-b589-15c5c8b4db02","order_by":0,"name":"Nadeem Ahmed","email":"","orcid":"","institution":"Indian Institute of Technology Roorkee","correspondingAuthor":false,"prefix":"","firstName":"Nadeem","middleName":"","lastName":"Ahmed","suffix":""},{"id":399140340,"identity":"d98aec77-0722-4250-9068-b7c158808583","order_by":1,"name":"Ram Prakash Bharti","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVRIiWNgGAWjYFACHjYwyc/M2AARYCZOiwGPZDNjYwNJWhgMDjDArCEAzGf3Hnvwc88fGePjzO2PKxjs5BnYeQ/g1SJz51y6Yc8zAx6zw4yNjWcYkg0bmPkS8GqRkMgxk+A5ANXSwMCcwMDMY0BQi+QfoBbjZrCWeuK0SINsMWAGazlMhBaZc2nSMgeMeSSADpvZYHDcsI2gFuneY5JvDsjZ8/cff/CxoaJanp//DH4tDBIoPKBiNvzqMbSMglEwCkbBKMACAAGxN9oVju1nAAAAAElFTkSuQmCC","orcid":"","institution":"Indian Institute of Technology Roorkee","correspondingAuthor":true,"prefix":"","firstName":"Ram","middleName":"Prakash","lastName":"Bharti","suffix":""},{"id":399140341,"identity":"783aff71-8cb4-4b82-bc29-e6bef3b31a93","order_by":2,"name":"Suneet Singh","email":"","orcid":"","institution":"Indian Institute of Technology Bombay","correspondingAuthor":false,"prefix":"","firstName":"Suneet","middleName":"","lastName":"Singh","suffix":""}],"badges":[],"createdAt":"2025-01-07 10:38:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5780462/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5780462/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00366-025-02177-1","type":"published","date":"2025-07-22T15:57:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":87756667,"identity":"d7025e14-7e1c-4216-b936-c6309c507c17","added_by":"auto","created_at":"2025-07-28 16:07:07","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":18552196,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5780462/v1_covered_6865d4c0-3c3a-490b-884f-932f5a2e4a4e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eEfficient Cell-centered Nodal Integral Method for Multi-dimensional Burgers’ Equations\u003c/p\u003e","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":"engineering-with-computers","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ewco","sideBox":"Learn more about [Engineering with Computers](http://link.springer.com/journal/366)","snPcode":"366","submissionUrl":"https://submission.nature.com/new-submission/366/3","title":"Engineering with Computers","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Burgers’ equations, Difference equations, Analytical nodal methods, Coarse-mesh methods, Cell-centered nodal integral method","lastPublishedDoi":"10.21203/rs.3.rs-5780462/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5780462/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"An efficient coarse-mesh nodal integral method (NIM), based on cell-centered variables and referred to as cell-centered NIM (CCNIM), is developed and applied for solving multi-dimensional, time-dependent, Burgers’ equations. 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