{"id":7044204,"date":"2026-08-22T19:36:06","date_gmt":"2026-08-22T19:36:06","guid":{"rendered":"https:\/\/peraltafinancing.com\/animation\/adaptive-fluid-cohomology-on-surfaces\/"},"modified":"2026-08-22T19:36:06","modified_gmt":"2026-08-22T19:36:06","slug":"adaptive-fluid-cohomology-on-surfaces","status":"publish","type":"post","link":"https:\/\/fivemor.com\/?p=7044204","title":{"rendered":"Adaptive Fluid Cohomology on Surfaces"},"content":{"rendered":"<p> <br \/>\n<\/p>\n<div id=\"post-4544\">\n<p>\t\t\t\t\t<!-- .entry-meta --><\/p>\n<div class=\"entry-content\">\n<p class=\"wp-block-paragraph\">Bastian Abt, David Stotko, Nils Wandel, Reinhard Klein<\/p>\n<p class=\"wp-block-paragraph\">Simulating inviscid, incompressible fluids on non-simply-connected curved surfaces requires careful treatment of the flow\u2019s local and global behavior. While recent theoretical advancements have established the critical dynamics of the harmonic component in such flows, practical applications remain computationally restricted by a lack of spatial and temporal adaptivity. Furthermore, simulations on poor-quality meshes often lead to numerical instability and a failure to preserve the flow\u2019s underlying harmonic component when using naive interpolation methods. In this paper, we introduce Adaptive Fluid Cohomology, a framework that integrates dynamic spatial and temporal refinement into the simulation of the Euler equations. We leverage a posteriori error estimation to adjust spatial resolution on the fly, alongside a standard Dormand-Prince 5(4) time-stepping scheme for temporal accuracy. To ensure stability during mesh mutations, we develop a novel method that robustly transfers the harmonic basis during remeshing. While our experimental evaluation focuses on 2D surface flows, the underlying theoretical formulation is presented to capture the 3D setting as well. Our evaluation demonstrates that this adaptive approach accurately recreates the dynamics of high-resolution simulations while reducing the memory footprint by up to <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow><mn>86<\/mn><mtext>\u2009<\/mtext><mi mathvariant=\"normal\">%<\/mi><\/mrow>86\\,\\%<\/math>86% and maintaining numerical stability even on poor-quality triangulations where static methods fail.<\/p>\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/kandel.informatik.uni-bonn.de\/publications\/abt-2026-adaptive\">Adaptive Fluid Cohomology on Surfaces<\/a><\/p>\n<\/p><\/div>\n<p><!-- .entry-content --><\/p>\n<div class=\"entry-utility\">\n\t\t\t\t\t\t\tThis entry was posted in <a href=\"https:\/\/www.physicsbasedanimation.com\/category\/uncategorized\/\" rel=\"category tag\">Uncategorized<\/a>. Bookmark the <a href=\"https:\/\/www.physicsbasedanimation.com\/2026\/07\/17\/adaptive-fluid-cohomology-on-surfaces\/\" title=\"Permalink to Adaptive Fluid Cohomology on Surfaces\" rel=\"bookmark\">permalink<\/a>.\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n<p><!-- .entry-utility -->\n\t\t\t\t\t<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Bastian Abt, David Stotko, Nils Wandel, Reinhard Klein Simulating inviscid, incompressible fluids on non-simply-connected curved surfaces requires careful treatment of the flow\u2019s local and global behavior. While recent theoretical advancements have established the critical dynamics of the harmonic component in such flows, practical applications remain computationally restricted by a lack of spatial and temporal adaptivity. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":354832,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12035],"tags":[17108,206616,3081,22416],"dealstore":[],"offerexpiration":[],"class_list":["post-7044204","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-animation","tag-adaptive","tag-cohomology","tag-fluid","tag-surfaces"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Adaptive Fluid Cohomology on Surfaces - Som2ny Network<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fivemor.com\/?p=7044204\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Adaptive Fluid Cohomology on Surfaces - Som2ny Network\" \/>\n<meta property=\"og:description\" content=\"Bastian Abt, David Stotko, Nils Wandel, Reinhard Klein Simulating inviscid, incompressible fluids on non-simply-connected curved surfaces requires careful treatment of the flow\u2019s local and global behavior. While recent theoretical advancements have established the critical dynamics of the harmonic component in such flows, practical applications remain computationally restricted by a lack of spatial and temporal adaptivity. 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