FASTEST - A new high order FV method dynamically locally self h-adaptive for convective-diffusive problems

FASTEST - A new high order FV method dynamically locally self h-adaptive for convective-diffusive problems | 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 FASTEST - A new high order FV method dynamically locally self h-adaptive for convective-diffusive problems Vincenzo A. Pennati, Antoine C. Kengni Jotsa, Jacques Tagoudjeu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6278611/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 In this article a new finite volume method for the numerical solution of convective-diffusive 1D problems is developed. It is conservative, high order in time and space, allows the partitioning of the domain by equal or unequal finite volumes, thus dynamically locally self h-adaptive. The definition of the monotonic profiles is accomplished by means of cubic weighted ν -splines and Taylor expansions. The profile analysis is conducted in the normalized plane with the velocity varying in time and space. Moreover the flux is assigned by Upwind or by second order back-ward Characteristics if the estimated flux is outside of the unit square or the transformation into the normalized plane is not possible, respectively. The formulation of dynamically locally self h-adaptive processes is designed to achieve the dual purpose to increase the accuracy and to keep as small as possible the number of finite volumes. The initial-boundary stability and convergence properties of the new method are examined in detail, also in presence of h-adaptivity. In addition, a generalization of the new scheme to 2D and 3D problems is presented. Finally, some numerical test are carried out to verify the properties of the new method, including two CFD problems. Mathematics Subject Classification: 65M08, 65M12, 65N08, 65N12, 65N22, 65N50, 76M12 Applied Mathematics FV method for convective-diffusive problems Stability and convergence for initial-boundary problems High order monotonic profiles Dynamically locally self h-adaptive method 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. 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-6278611","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":432169636,"identity":"5231b7fd-4a52-4a60-8c35-e608e4743896","order_by":0,"name":"Vincenzo A. 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It is conservative, high order in time and space, allows the partitioning of the domain by equal or unequal finite volumes, thus dynamically locally self h-adaptive. The definition of the monotonic profiles is accomplished by means of cubic weighted \u003cem\u003eν\u003c/em\u003e-splines and Taylor expansions. The profile analysis is conducted in the normalized plane with the velocity varying in time and space. Moreover the flux is assigned by Upwind or by second order back-ward Characteristics if the estimated flux is outside of the unit square or the transformation into the normalized plane is not possible, respectively. The formulation of dynamically locally self h-adaptive processes is designed to achieve the dual purpose to increase the accuracy and to keep as small as possible the number of finite volumes. The initial-boundary stability and convergence properties of the new method are examined in detail, also in presence of h-adaptivity. In addition, a generalization of the new scheme to 2D and 3D problems is presented. 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