Comparison of computational advantages of high-order discontinuous Galerkin and conventional finite-volume dynamical cores in atmospheric turbulent simulations

Comparison of computational advantages of high-order discontinuous Galerkin and conventional finite-volume dynamical cores in atmospheric turbulent simulations | 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 Article Comparison of computational advantages of high-order discontinuous Galerkin and conventional finite-volume dynamical cores in atmospheric turbulent simulations Yuta Kawai, Xuanzhengbo Ren, Seiya Nishizawa, Takahiro Katagiri, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8869129/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This study discusses the computational advantages of high-order dynamical cores over a conventional low-order dynamical core in atmospheric turbulent simulations. Implicit and explicit large-eddy simulations (LES) of dry Rayleigh convection were performed using two dynamical cores: one based on a high-order discontinuous Galerkin method (DGM) and the other on a totally second-order conventional finite-volume method (FVM) with advection schemes of various orders. The effective resolution and numerical energy accumulation, derived from kinetic energy spectra, were used to evaluate the physical performance of both dynamical cores. In the implicit LES experiment, we confirmed that the high-order DGM with a polynomial order of p=11 achieved a finer effective resolution than the FVM with third-order and seventh-order upwind schemes (UD3 and UD7). In contrast, in the explicit LES experiment, the effective resolution was largely determined by the subgrid-scale turbulence model, thereby reducing the relative advantage of high-order schemes. Our cost metrics, which combine the physical performance and computational resource usage, demonstrate that the DGM with p=7, 11 and the FVM with UD7 can achieve lower overall computational costs than the FVM with UD3 in both implicit and explicit LES experiments. Although the high-order DGM requires larger computational resources due to a stricter CFL condition, its overall computational costs are reduced in the implicit LES experiment because of its finer effective resolution, as well as high computational efficiency associated with superior data locality and smaller inter-node communication overhead. On the other hand, to fully exploit the advantages of high-order schemes in explicit LES, it is necessary to redesign the turbulence model so that the filter length becomes consistent with the inherent effective resolution of the dynamical cores, and to relax the stricter CFL condition for the DGM. Atmospheric dynamical core High-order scheme Discontinuous Galerkin method Finite volume method Turbulent simulation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 13 Apr, 2026 Reviews received at journal 12 Apr, 2026 Reviewers agreed at journal 19 Mar, 2026 Reviews received at journal 03 Mar, 2026 Reviewers agreed at journal 22 Feb, 2026 Reviewers invited by journal 20 Feb, 2026 Editor assigned by journal 13 Feb, 2026 Submission checks completed at journal 13 Feb, 2026 First submitted to journal 13 Feb, 2026 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-8869129","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":595273003,"identity":"e8cfc856-606b-43f8-b448-0b1b4c4a5533","order_by":0,"name":"Yuta Kawai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYNCCA0DMzHyAIeEAjIcXMMO0sCWQqoWBx4AI1UBgcCP/4AeGM3aJ/e083z48OGOTx8B4Fr9GgxvJzBIMN5ITZxzm3Twj4UZaMQPDuQRCWhgkGD4w5zYAtTAkfDic2MBwxoCgLT8YPtTnzj/M8xio5T9RWtiADjucu+EwDzNDwo0DhLVInnlsZpFw5nj9xsNsxgwJZ5IT2wj5he944uMbH45VG8udP/yY8ccxYNBJEAgxBZA0iqlsEmfw6mCQb8AQ4u/Br2UUjIJRMApGHAAAx1dTGa7n9U8AAAAASUVORK5CYII=","orcid":"","institution":"RIKEN Center for Computational Science","correspondingAuthor":true,"prefix":"","firstName":"Yuta","middleName":"","lastName":"Kawai","suffix":""},{"id":595273004,"identity":"a92ffd1b-0846-4b34-ba7a-7ac7e7683b41","order_by":1,"name":"Xuanzhengbo Ren","email":"","orcid":"","institution":"Nagoya University","correspondingAuthor":false,"prefix":"","firstName":"Xuanzhengbo","middleName":"","lastName":"Ren","suffix":""},{"id":595273005,"identity":"06f501cc-5b37-434f-99ce-ea5053573c4e","order_by":2,"name":"Seiya Nishizawa","email":"","orcid":"","institution":"RIKEN Center for Computational Science","correspondingAuthor":false,"prefix":"","firstName":"Seiya","middleName":"","lastName":"Nishizawa","suffix":""},{"id":595273006,"identity":"a139e074-16dc-4977-a128-3e6105855381","order_by":3,"name":"Takahiro Katagiri","email":"","orcid":"","institution":"Nagoya University","correspondingAuthor":false,"prefix":"","firstName":"Takahiro","middleName":"","lastName":"Katagiri","suffix":""},{"id":595273007,"identity":"c33c7a13-0c9f-4bbb-84d0-b55daa0b58ea","order_by":4,"name":"Hirofumi Tomita","email":"","orcid":"","institution":"RIKEN Center for Computational Science","correspondingAuthor":false,"prefix":"","firstName":"Hirofumi","middleName":"","lastName":"Tomita","suffix":""}],"badges":[],"createdAt":"2026-02-13 08:09:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8869129/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8869129/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103506189,"identity":"1bf8f916-26bb-4eea-b458-18ec66e8404c","added_by":"auto","created_at":"2026-02-26 13:34:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5476223,"visible":true,"origin":"","legend":"","description":"","filename":"src.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8869129/v1_covered_c469efc8-89c5-49d8-8742-de410b19e9f4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Comparison of computational advantages of high-order discontinuous Galerkin and conventional finite-volume dynamical cores in atmospheric turbulent simulations","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-meteorological-society-of-japan","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"44394","submissionUrl":"https://submission.springernature.com/new-submission/44394/3","title":"Journal of the Meteorological Society of Japan","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Atmospheric dynamical core, High-order scheme, Discontinuous Galerkin method, Finite volume method, Turbulent simulation","lastPublishedDoi":"10.21203/rs.3.rs-8869129/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8869129/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study discusses the computational advantages of high-order dynamical cores over a conventional low-order dynamical core in atmospheric turbulent simulations. Implicit and explicit large-eddy simulations (LES) of dry Rayleigh convection were performed using two dynamical cores: one based on a high-order discontinuous Galerkin method (DGM) and the other on a totally second-order conventional finite-volume method (FVM) with advection schemes of various orders. The effective resolution and numerical energy accumulation, derived from kinetic energy spectra, were used to evaluate the physical performance of both dynamical cores. In the implicit LES experiment, we confirmed that the high-order DGM with a polynomial order of p=11 achieved a finer effective resolution than the FVM with third-order and seventh-order upwind schemes (UD3 and UD7). In contrast, in the explicit LES experiment, the effective resolution was largely determined by the subgrid-scale turbulence model, thereby reducing the relative advantage of high-order schemes. Our cost metrics, which combine the physical performance and computational resource usage, demonstrate that the DGM with p=7, 11 and the FVM with UD7 can achieve lower overall computational costs than the FVM with UD3 in both implicit and explicit LES experiments. Although the high-order DGM requires larger computational resources due to a stricter CFL condition, its overall computational costs are reduced in the implicit LES experiment because of its finer effective resolution, as well as high computational efficiency associated with superior data locality and smaller inter-node communication overhead. 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