The Role of Advection and Diffusion Terms on the Concentration of Dissolved Oxygen in River Pollution

The Role of Advection and Diffusion Terms on the Concentration of Dissolved Oxygen in River Pollution | 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 The Role of Advection and Diffusion Terms on the Concentration of Dissolved Oxygen in River Pollution Tsegaye Simon Lachamo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7941552/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 Dissolved oxygen concentration (DOC) is a crucial metric for assessing and monitoring the overall quality of a water body. A mathematical model utilizes various water quality parameters as inputs to evaluate, monitor, and manage DOC, offering valuable insights into river water quality. Specifically, we propose modeling the transport of DOC using a time-dependent 1-D linear advection-diffusion equation (ADE), subject to defined initial and boundary conditions. To obtain numerical solutions, we applied two different methods: the finite element scheme (FES) and the Taylor-Galerkin scheme. Our results show that the FES is appropriate for problems where diffusion is the dominant effect. However, we observed that as advection becomes dominant, the FES becomes unstable and difficult to evaluate. Consequently, the Taylor-Galerkin schemewas designed and employed as an alternative approach. From the simulation results, we conclude that increasing parameters such as river velocity (w), the diffusion coefficient (d), and the combined advection-diffusion effect all contribute to significantly faster DO transport within the river over a shorter period. Applied Mathematics Finite element scheme Advection-diffusion equation DOC River Pollution Taylor Galerkin scheme Full Text Additional Declarations The authors declare no competing interests. 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. 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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-7941552","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":534556785,"identity":"cfe2f2ab-bc4a-462c-8f76-95dac6c9371e","order_by":0,"name":"Tsegaye Simon 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Pollution\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Kotebe University of Education","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":"Finite element scheme, Advection-diffusion 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A mathematical model utilizes various water quality parameters as inputs to evaluate, monitor, and manage DOC, offering valuable insights into river water quality. Specifically, we propose modeling the transport of DOC using a time-dependent 1-D linear advection-diffusion equation (ADE), subject to defined initial and boundary conditions. To obtain numerical solutions, we applied two different methods: the finite element scheme (FES) and the Taylor-Galerkin scheme. Our results show that the FES is appropriate for problems where diffusion is the dominant effect. However, we observed that as advection becomes dominant, the FES becomes unstable and difficult to evaluate. Consequently, the Taylor-Galerkin schemewas designed and employed as an alternative approach. 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