Modelling Sediment Transport and Chemical Dissolution in a One-Dimensional River System: An Advection–Diffusion–Reaction Approach with Nonlinear Velocity Coupling

Modelling Sediment Transport and Chemical Dissolution in a One-Dimensional River System: An Advection–Diffusion–Reaction Approach with Nonlinear Velocity Coupling | 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 Method Article Modelling Sediment Transport and Chemical Dissolution in a One-Dimensional River System: An Advection–Diffusion–Reaction Approach with Nonlinear Velocity Coupling Silas Alebikenaba Ayariga, NJINGA Morelle, Bassirou Lo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9683971/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, analyses, and simulates a coupled advection–diffusion–reaction (ADR) model describing the interaction between suspended sediment and a dissolved chemical substance in a one-dimensional river reach [0, L]. The state variables S(x, t) and C(x, t), representing the sediment and chemical concentrations in kg·m⁻³, are governed by a system of two nonlinear parabolic partial differential equations. Two physically motivated features enrich the classical ADR framework: (i) a turbulent dispersion term for the sediment (Dₛ > 0), which renders the system fully parabolic and prevents shock formation; and (ii) a nonlinear velocity law v(S) = v₀(1 − αS), which couples transport speed directly to sediment concentration, creating a self-reinforcing feedback between sediment erosion and flow speed. Well-posedness of the initial–boundary value problem is established via a structural argument relying on strict parabolicity, the parabolic maximum principle, and the Gronwall lemma. Numerical simulations using an implicit BDF scheme confirm that the sediment inventory decreases by approximately 16% over a 10-hour window as the chemical front advances downstream. A 500-run Latin Hypercube Sampling / Partial Rank Correlation Coefficient (LHS–PRCC) sensitivity analysis identifies μₛᶜ, v₀, α, and μᶜ as the dominant parameters, while diffusion coefficients play negligible roles on the simulated time scale. Computational Mathematics Applied Mathematics Mathematical Physics sediment transport advection–diffusion–reaction chemical dissolution nonlinear velocity coupling coupled PDEs well-posedness Latin Hypercube Sampling PRCC river modelling. 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. 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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-9683971","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":638541726,"identity":"c2032ecf-c488-4d21-8015-cadc9526d017","order_by":0,"name":"Silas Alebikenaba Ayariga","email":"data:image/png;base64,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","orcid":"","institution":"African Institute for Mathematical Sciences, Senegal","correspondingAuthor":true,"prefix":"","firstName":"Silas","middleName":"Alebikenaba","lastName":"Ayariga","suffix":""},{"id":638541727,"identity":"1a690f6e-fb8c-4ab9-9f37-23b8b3a6a22a","order_by":1,"name":"NJINGA Morelle","email":"","orcid":"","institution":"African Institute for Mathematical Sciences, Senegal","correspondingAuthor":false,"prefix":"","firstName":"NJINGA","middleName":"","lastName":"Morelle","suffix":""},{"id":638541728,"identity":"a6186f78-ee4d-4b7f-bb15-e95193b5d3b0","order_by":2,"name":"Bassirou Lo","email":"","orcid":"","institution":"African Institute for Mathematical Sciences, Senegal","correspondingAuthor":false,"prefix":"","firstName":"Bassirou","middleName":"","lastName":"Lo","suffix":""}],"badges":[],"createdAt":"2026-05-11 20:29:44","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9683971/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9683971/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109172124,"identity":"9778d39a-c056-4ac3-9b28-ad3fdc302697","added_by":"auto","created_at":"2026-05-13 09:03:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":535440,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptSedimentChemicalADR.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9683971/v1_covered_afac01bd-f811-4f58-8770-6f560371291f.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eModelling Sediment Transport and Chemical Dissolution in a One-Dimensional River System: \u003c/strong\u003e\u003cem\u003eAn Advection–Diffusion–Reaction Approach with Nonlinear Velocity Coupling\u003c/em\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":" sediment transport, advection–diffusion–reaction, chemical dissolution, nonlinear velocity coupling, coupled PDEs, well-posedness, Latin Hypercube Sampling, PRCC, river modelling.","lastPublishedDoi":"10.21203/rs.3.rs-9683971/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9683971/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cem\u003eThis paper presents, analyses, and simulates a coupled advection–diffusion–reaction (ADR) model describing the interaction between suspended sediment and a dissolved chemical substance in a one-dimensional river reach [0, L]. 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