Numerical Analysis and Testing of Efficient Ensemble Eddy Viscosity Algorithms for high-Reynolds-number Stochastic Flow Problems

Numerical Analysis and Testing of Efficient Ensemble Eddy Viscosity Algorithms for high-Reynolds-number Stochastic Flow 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 Numerical Analysis and Testing of Efficient Ensemble Eddy Viscosity Algorithms for high-Reynolds-number Stochastic Flow Problems Brandiece N Berry, Md Mahmudul Islam, Muhammad Mohebujjaman, Neethu Suma Raveendran This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8437203/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 paper, we first propose a continuous Ensemble Eddy Viscosity (EEV) model for stochastic flow problems and then introduce a family of fully discrete, grad-div–regularized, efficient ensemble parameterized schemes for this model. The linearized Implicit-Explicit (IMEX) EEV generic algorithm shares a common coefficient matrix for each realization per time-step, but with different right-hand side vectors, which reduces the computational cost and memory requirements to the order of solving deterministic flow problems. Two family members of the proposed time-stepping algorithm are analyzed and proven to be stable. It is found that one is first-order and the other is second-order accurate in time for any stable finite element pairs. Avoiding the discrete inverse inequality, the optimal convergence of both schemes is proven rigorously for both 2D and 3D problems. For appropriately large grad-div parameters, both schemes are unconditionally stable and allow weakly divergence-free elements. The convergence rates are verified numerically using manufactured solutions with high expected Reynolds numbers E[Re]=103,104, 105 ,and 106. For various high E[Re], the schemes are implemented on benchmark problems and are found to perform well. These include a 2D channel flow over a unit step problem, a 2D channel flow past a cylinder problem, a 2D Regularized Lid-Driven Cavity (RLDC) problem examined using a non-intrusive Stochastic Collocation Method (SCM), and a 3D RLDC problem. High-Reynolds number uncertainty quantification fast ensemble calculation finite element method ensemble eddy viscosity stochastic flow problems 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. 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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-8437203","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":569514627,"identity":"8e24f06d-b245-41f5-b5c0-27f9934dc608","order_by":0,"name":"Brandiece N Berry","email":"","orcid":"","institution":"University of Alabama at Birmingham","correspondingAuthor":false,"prefix":"","firstName":"Brandiece","middleName":"N","lastName":"Berry","suffix":""},{"id":569514628,"identity":"0657a6e2-9d3c-409d-a8c6-30ad4f4f7bb4","order_by":1,"name":"Md Mahmudul Islam","email":"","orcid":"","institution":"University of Alabama at 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