Research on high-order flux reconstruction method with adaptive mesh for shock capturing

Research on high-order flux reconstruction method with adaptive mesh for shock capturing | 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 Research on high-order flux reconstruction method with adaptive mesh for shock capturing Xiuqiang Ma, Jian Xia, Hao Fu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-31697/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 High order schemes have been developed for a quite long time, and many famous schemes arise like Discontinuous Galerkin (DG), Spectral Difference (SD) and WENO schemes, etc. The Flux Reconstruction (FR) scheme proposed by Huynh has attracted the attention of researchers for its simplicity and efficiency. It’s written in differential form and bridges the DG and SD schemes, which can be constructed with a proper choice of parameter. In this paper, realize FR scheme based on the framework of the open source Adaptive Mesh Refinement (AMR) library p4est. To capture shock sharply, the performance of Localized Laplacian Artificial Viscosity (LLAV) and In-cell Piecewise Integrated Solution methods are compared. As an important way of reducing computational cost, AMR technique integrated in p4est is also combined with FR. The performance of the developed code is tested in both one dimensional and two dimensional and get some quite attracting results. Aeronautics and Astronautics Flux Reconstruction Shock capturing Artificial Diffusivity In-cell Piecewise Integrated Solution Adaptive Mesh Refinement Full Text 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-31697","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research","associatedPublications":[],"authors":[{"id":611597,"identity":"884b01e4-e25f-47cf-bcc0-4dbcfbb32f7d","order_by":0,"name":"Xiuqiang Ma","email":"","orcid":"","institution":"Nanjing University of Aeronautics and Astronautics College of Aerospace Engineering","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xiuqiang","middleName":"","lastName":"Ma","suffix":""},{"id":611598,"identity":"a8143855-ee83-4b50-822a-f567dd47c198","order_by":1,"name":"Jian 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