Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization

Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization | 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 Rotational shallow water equations with viscous damping and boundary control: structure-preserving spatial discretization Flávio Luiz Cardoso-Ribeiro, Ghislain Haine, Laurent Lefèvre, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3006274/v2 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Nov, 2024 Read the published version in Mathematics of Control, Signals, and Systems → Version 2 posted 8 You are reading this latest preprint version Show more versions Abstract This paper is dedicated to structure-preserving spatial discretization of shallow water dynamics. First, a port-Hamiltonian formulation is provided for the two-dimensional rotational shallow water equations with viscous damping. Both tangential and normal boundary port variables are introduced. Then the corresponding weak form is derived and a partitioned finite element method is applied to obtain a finite-dimensional continuous-time port-Hamiltonian approximation. Four simulation scenarios are investigated to illustrate the approach and show its effectiveness. Full Text Additional Declarations No competing interests reported. Supplementary Files movieviscous.ogv movierotating.ogv movieinviscid.ogv movieemptying.ogv Cite Share Download PDF Status: Published Journal Publication published 28 Nov, 2024 Read the published version in Mathematics of Control, Signals, and Systems → Version 2 posted Editorial decision: Revision requested 01 May, 2024 Reviews received at journal 12 Apr, 2024 Reviewers agreed at journal 12 Feb, 2024 Reviews received at journal 23 Jan, 2024 Reviewers agreed at journal 27 Dec, 2023 Reviewers invited by journal 22 Dec, 2023 Submission checks completed at journal 22 Dec, 2023 First submitted to journal 21 Dec, 2023 You are reading this latest preprint version Show more versions 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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