Efficient and long-time accurate partitioned method with multirate time steps for the nonstationary Stokes-Darcy model

Efficient and long-time accurate partitioned method with multirate time steps for the nonstationary Stokes-Darcy model | 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 and long-time accurate partitioned method with multirate time steps for the nonstationary Stokes-Darcy model Guangzhi Du, Liyun Zuo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8820518/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 study investigates a multirate, decoupled scheme that adopts different time steps in different physical problem subdomains for the unsteady Stokes-Darcy system with the Beavers-Joseph interface condition. Under a modest time step constraint of the form $\Delta t\leq C$(phiysical parameters,$r$), we prove that the proposed algorithm is unconditional and long-time (over $0\leq t <\infty$) stability. Based on this, we establish the optimal error estimation which is uniformly bounded in time over $0\leq t <\infty$. Some numerical experiments are reported to demonstrate the theoretical results. MSC: 65M55, 65M12, 65M15, 65M60, 35Q35, 76D07, 76S05 Stokes-Darcy system multiple-time-step domain decomposition method unconditional stability long-time stability uniform in time error estimate 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. 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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-8820518","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599039295,"identity":"7b4f5cfe-6b7d-43f3-9ca9-18ca458bcf4b","order_by":0,"name":"Guangzhi Du","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYHACA4YPDMxglgTRWhhnkKyFmYckLfL+h7dJ2/yxzjM4wHzwNg+DXR5BLYYHjpVJ57alFxscYEu25mFILiaspbHHTDq34XDihgM8ZtI8DAcSGwhqaQaqtPgD0sL/jTgt8mxALQxsYFvYiNNiwMNWbNnblp448zCbseUcg2QibOk/vPHGjz/WiX3Hmx/eeFNhR4QtB2AscNQYEFIPsoWgoaNgFIyCUTAKAPtGN+zjLYMNAAAAAElFTkSuQmCC","orcid":"","institution":"Shandong Normal University","correspondingAuthor":true,"prefix":"","firstName":"Guangzhi","middleName":"","lastName":"Du","suffix":""},{"id":599039296,"identity":"b6f705bb-5cd4-49eb-964b-2da3a9eac733","order_by":1,"name":"Liyun Zuo","email":"","orcid":"","institution":"University of Jinan","correspondingAuthor":false,"prefix":"","firstName":"Liyun","middleName":"","lastName":"Zuo","suffix":""}],"badges":[],"createdAt":"2026-02-08 09:25:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8820518/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8820518/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103821889,"identity":"b58624db-7e29-4fb3-b5e2-3490d99a27ca","added_by":"auto","created_at":"2026-03-03 10:25:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1002702,"visible":true,"origin":"","legend":"","description":"","filename":"SDBJdifferenttimesteps.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8820518/v1_covered_1e08c566-2960-4722-a8e4-bff6e20b9459.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Efficient and long-time accurate partitioned method with multirate time steps for the nonstationary Stokes-Darcy model","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":"Stokes-Darcy system, multiple-time-step, domain decomposition method, unconditional stability, long-time stability, uniform in time error estimate","lastPublishedDoi":"10.21203/rs.3.rs-8820518/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8820518/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates a multirate, decoupled scheme that adopts different time steps in \u0026nbsp;different physical problem subdomains for the unsteady Stokes-Darcy system with the Beavers-Joseph interface condition. Under a modest time step constraint of the form $\\Delta t\\leq C$(phiysical \u0026nbsp;parameters,$r$), we prove that the proposed algorithm is unconditional and long-time (over $0\\leq t \u0026lt;\\infty$) stability. Based on this, we establish the optimal error estimation which is uniformly bounded in time over $0\\leq t \u0026lt;\\infty$. Some numerical experiments are reported to demonstrate the theoretical results.\u003c/p\u003e\n\u003cp\u003eMSC: 65M55, 65M12, 65M15, 65M60, 35Q35, 76D07, 76S05\u003c/p\u003e","manuscriptTitle":"Efficient and long-time accurate partitioned method with multirate time steps for the nonstationary Stokes-Darcy model","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-03 10:24:00","doi":"10.21203/rs.3.rs-8820518/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"4195c92b-09b5-4237-bcf0-434cf1432fdf","owner":[],"postedDate":"March 3rd, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-18T10:28:08+00:00","index":12,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-03T10:24:00+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-03 10:24:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8820518","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8820518","identity":"rs-8820518","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}