T-PRIME: Taylor Physics-Regularized Inference for Mapping Eulerian Fields from PTV Data

T-PRIME: Taylor Physics-Regularized Inference for Mapping Eulerian Fields from PTV Data | 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 T-PRIME: Taylor Physics-Regularized Inference for Mapping Eulerian Fields from PTV Data Yang Zhang, Mahyar Moaven, Shreeju Banjade, Douglas W. Carter, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9533988/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract We introduce T-PRIME, a T aylor-series based P hysics- R egularized I nference framework for M apping E ulerian Fields from particle-based measurements, including particle positions, velocities, and material accelerations. The method embeds the incompressible Navier–Stokes momentum equations as linear constraints within a weighted least-squares formulation, yielding locally consistent estimates from irregularly distributed PTV data. Quantitative assessment using direct numerical simulation (DNS) data from the JHU turbulence database demonstrates accurate reconstruction of velocity-gradient-related quantities, including vorticity, \((Q)\) , and local pressure gradients, as well as coherent structures and near-wall features. Velocity Hessians can also be recovered within the same framework when higher-order derivatives are needed. Experimental results from a turbulent water jet and a turbulent flat-plate shear layer in air are used as comparative benchmarks against VIC \((#)\) , showing agreement in dominant structures and modal content while maintaining significantly lower per-snapshot computational cost for the cases examined. The approach provides a computationally efficient tool for mapping Lagrangian particle measurements to Eulerian representations suitable for velocity-gradient-based diagnostics and pressure reconstruction. PTV Physics-Informed Data assimilation Eulerian Mapping Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 05 May, 2026 Reviewers invited by journal 28 Apr, 2026 Editor assigned by journal 27 Apr, 2026 Submission checks completed at journal 27 Apr, 2026 First submitted to journal 26 Apr, 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. 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-9533988","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":635072714,"identity":"1390d4f1-0819-4049-8520-0575eb834a8a","order_by":0,"name":"Yang Zhang","email":"data:image/png;base64,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","orcid":"","institution":"Illinois Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Yang","middleName":"","lastName":"Zhang","suffix":""},{"id":635072720,"identity":"5d778f5c-4bbb-4a44-abef-6d0cc5fc578f","order_by":1,"name":"Mahyar Moaven","email":"","orcid":"","institution":"Illinois Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Mahyar","middleName":"","lastName":"Moaven","suffix":""},{"id":635072725,"identity":"da76c2da-c3d0-48ef-9a17-584ea4b29a7a","order_by":2,"name":"Shreeju Banjade","email":"","orcid":"","institution":"Illinois Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Shreeju","middleName":"","lastName":"Banjade","suffix":""},{"id":635072726,"identity":"e46863bb-39ff-4503-b835-68bfea4730f1","order_by":3,"name":"Douglas W. 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The method embeds the incompressible Navier\u0026ndash;Stokes momentum equations as linear constraints within a weighted least-squares formulation, yielding locally consistent estimates from irregularly distributed PTV data. Quantitative assessment using direct numerical simulation (DNS) data from the JHU turbulence database demonstrates accurate reconstruction of velocity-gradient-related quantities, including vorticity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((Q)\\)\u003c/span\u003e\u003c/span\u003e, and local pressure gradients, as well as coherent structures and near-wall features. Velocity Hessians can also be recovered within the same framework when higher-order derivatives are needed. Experimental results from a turbulent water jet and a turbulent flat-plate shear layer in air are used as comparative benchmarks against VIC\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((#)\\)\u003c/span\u003e\u003c/span\u003e, showing agreement in dominant structures and modal content while maintaining significantly lower per-snapshot computational cost for the cases examined. 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