Model-Adaptive Simulation of Hyperbolic Moment Equations in One Dimension

Model-Adaptive Simulation of Hyperbolic Moment Equations in One Dimension | 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 Model-Adaptive Simulation of Hyperbolic Moment Equations in One Dimension Rik Verbiest, Julian Koellermeier This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9180382/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 The need for space- and time-adaptivity in rarefied gas simulations arises because different time-variable subdomains within a rarefied gas domain often require varying levels of modelling complexity. Different-order moment models are effective at describing rarefied gas flows with respective levels of complexity in each subdomain. In this work, a numerical method for the model-adaptive simulation of the non-linear Hyperbolic Moment Equations (HME) model is proposed to simulate a rarefied gas flow using an HME model with time- and space-dependent model order. The first step of the adaptive procedure is a domain decomposition into subdomains each modelled by an HME model of an appropriate order, using domain decomposition criteria that are based on the exact model difference between a higher-order HME model and a lower-order HME model and on chosen error thresholds. In the second step of the adaptive procedure, a non-linear adaptation of a recently developed padded buffer cell approach is presented to couple these varying-order HME models using a single finite volume scheme. Finally, a smoothing of the domain decomposition is proposed to limit oscillations generated by the coupling. While its performance depends on the thresholds and the smoothing parameter, the proposed model-adaptive simulation method yields accurate results while obtaining computational speedups of up to 40 percent compared to using a high-order HME model in the entire domain. moment models multi-scale modelling nonequilibrium gas flows adaptive 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. 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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-9180382","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":612123858,"identity":"98159a48-8979-4ba7-901f-0312e0bbc0b4","order_by":0,"name":"Rik Verbiest","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVRIiWNgGAWjYLACxgYJIMl8AMzhI14LG1sCmMNGpBaQUh4D4rSYN/AYPq7cYSEnP7/n22eeXwx5BLXIHOAxNjx7RsLY4Bjv5tm8fQzFBLVIMLClSTa2SSRuYOPdzMzbw5DYRoSW9J9ALfXz23geE6uF+RgjUEsCwzEeZmaeH8RoYWY+LNl4RsJww7E0Y8a5DRJEaGFvbPzYuKNOXr758GOGN39sEvsJaWFgRuYwtkkQ1IAO/pCsYxSMglEwCkYAAAB3pjRqJevunwAAAABJRU5ErkJggg==","orcid":"","institution":"University of Groningen","correspondingAuthor":true,"prefix":"","firstName":"Rik","middleName":"","lastName":"Verbiest","suffix":""},{"id":612123859,"identity":"9c64db34-7950-44b7-8f87-f243a3685d0a","order_by":1,"name":"Julian Koellermeier","email":"","orcid":"","institution":"Ghent University","correspondingAuthor":false,"prefix":"","firstName":"Julian","middleName":"","lastName":"Koellermeier","suffix":""}],"badges":[],"createdAt":"2026-03-20 15:38:15","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-9180382/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9180382/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105728773,"identity":"a99070bd-fd4a-4ac9-abb5-297f64716a88","added_by":"auto","created_at":"2026-03-30 11:12:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3082830,"visible":true,"origin":"","legend":"","description":"","filename":"modelAdaptiveHME1D.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9180382/v1_covered_3c341813-da50-49da-8862-eb53b0fec98f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Model-Adaptive Simulation of Hyperbolic Moment Equations in One Dimension","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":true,"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":"moment models, multi-scale modelling, nonequilibrium gas flows, adaptive simulation","lastPublishedDoi":"10.21203/rs.3.rs-9180382/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9180382/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The need for space- and time-adaptivity in rarefied gas simulations arises because different time-variable subdomains within a rarefied gas domain often require varying levels of modelling complexity. 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