A consistent projection method for the Micropolar Navier-Stokes equations

A consistent projection method for the Micropolar Navier-Stokes 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 A consistent projection method for the Micropolar Navier-Stokes equations Zhiyong Si, Ziyi Li, Yunxia Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9630157/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, we introduce a consistent projection method, namely the Gauge-Uzawa method, for the numerical solution of incompressible Micropolar Navier-Stokes Equations (MNSE). This method integrates the advantages of both gauge and Uzawa methodologies into a unified vari-ational framework. By adopting a fully discrete projection strategy, the scheme efficiently decouples the computations of velocity, angular velocity, and pressure fields—thus enhancing computational efficiency while maintaining numerical accuracy. We conduct a rigorous theoretical analysis of the proposed method, establishing its unconditional stability and deriving optimal error estimates for all primary variables (velocity, angular velocity, and pressure) under appropriate norms. Numerical experiments verify that the method achieves the expected convergence order across a series of test cases. The results are in excellent agreement with theoretical predictions, fully demonstrating the effectiveness and reliability of the proposed approach. Micropolar Navier-Stokes equations Consistent projection method Energy estimates Optimal error estimates Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-9630157","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":635473004,"identity":"2ea77177-d402-4e37-9c38-6cd9efb95ea9","order_by":0,"name":"Zhiyong Si","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYDACZgY2hgQQg70HzGdsIF4LzxlitTAAtYCBRA6RWuTb2Z89eNhmkycf+fbYYx4GG9kNB5ifPcCnxeAwQ7pBYltaseHtvHRjHoY04w0H2MwN8GphZjgmkdh2OHHj7BwzaR6Gw4kbDvCwSeB1WDNjG0TLzDMgLf8Ja2E4zMwG1jJfggek5QBhLQaH2dgkEs6lJW7gyTE3nGOQbDzzMJsZfof1H38m+aPMJnF++xmzB28q7GT7jjc/w+8wEGAERo3BAVAEgYKKmaB6EPgDtK4BFqejYBSMglEwCtAAAMwoRWgvWBeGAAAAAElFTkSuQmCC","orcid":"","institution":"Henan Polytechnic University","correspondingAuthor":true,"prefix":"","firstName":"Zhiyong","middleName":"","lastName":"Si","suffix":""},{"id":635473006,"identity":"f3a169d1-38bc-42a1-8eb3-7a0f04a01951","order_by":1,"name":"Ziyi Li","email":"","orcid":"","institution":"Henan Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Ziyi","middleName":"","lastName":"Li","suffix":""},{"id":635473013,"identity":"06d35201-0270-44ed-8522-68d5c544c457","order_by":2,"name":"Yunxia Wang","email":"","orcid":"","institution":"Henan Polytechnic University","correspondingAuthor":false,"prefix":"","firstName":"Yunxia","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2026-05-06 11:54:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9630157/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9630157/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108669173,"identity":"ceda9c03-92fd-4a35-b39b-072ec16e270d","added_by":"auto","created_at":"2026-05-07 07:12:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":265219,"visible":true,"origin":"","legend":"","description":"","filename":"repaper260402.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9630157/v1_covered_73026da1-c5c9-405f-bdce-6fcf4a6d5337.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eA consistent projection method for the Micropolar Navier-Stokes equations \u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Micropolar Navier-Stokes equations; Consistent projection method; Energy estimates; Optimal error estimates","lastPublishedDoi":"10.21203/rs.3.rs-9630157/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9630157/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, we introduce a consistent projection method, namely the Gauge-Uzawa method, for the numerical solution of incompressible Micropolar Navier-Stokes Equations (MNSE). 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