An h-Adaptive Finite Element Method for Transient Thermal Analysis in Laser-Based Additive Manufacturing

An h-Adaptive Finite Element Method for Transient Thermal Analysis in Laser-Based Additive Manufacturing | 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 An h-Adaptive Finite Element Method for Transient Thermal Analysis in Laser-Based Additive Manufacturing Olusola- Collins Akeremale, Olusegun - Adeyemi Olaiju, Mukaila Akinde, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7917928/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 This paper presents a transient 2D finite element solver with h-adaptive mesh refinement for simulating heat transfer in laser-based additive manufacturing (AM). The governing equation is the time-dependent heat conduction equation with a moving Gaussian heat source, modeling the laser beam interaction with powder bed material. A posteriori error estimation based on nodal temperature variation drives local mesh refinement around regions of steep thermal gradients. Linear triangularP 1 elements are used, and mesh regeneration via Delaunay triangulation ensures conformity after each refinement step. The temporal discretization is performed using the implicit Euler method, and the solution is prolonged to the new mesh using nearest-neighbor interpolation. Numerical results demonstrate accurate resolution of the moving melt pool and exponential decay in element-wise error indicators under adaptive refinement. The method is well-suited for simulating laser scanning processes in AM with high spatial and temporal accuracy while maintaining computational efficiency. Adaptive Finite Element Method Transient Heat Conduction Moving Heat Source h-Adaptive Mesh Refinement Numerical Simulation 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-7917928","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":545864647,"identity":"039029c2-5db8-470d-a3a0-22c93835447e","order_by":0,"name":"Olusola- Collins 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Manufacturing","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"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":"Adaptive Finite Element Method, Transient Heat Conduction, Moving Heat Source, h-Adaptive Mesh 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The governing equation is the time-dependent heat conduction equation with a moving Gaussian heat source, modeling the laser beam interaction with powder bed material. A posteriori error estimation based on nodal temperature variation drives local mesh refinement around regions of steep thermal gradients. Linear triangularP\u003csub\u003e1\u003c/sub\u003e elements are used, and mesh regeneration via Delaunay triangulation ensures conformity after each refinement step. The temporal discretization is performed using the implicit Euler method, and the solution is prolonged to the new mesh using nearest-neighbor interpolation. Numerical results demonstrate accurate resolution of the moving melt pool and exponential decay in element-wise error indicators under adaptive refinement. 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