{"id":7076741,"date":"2026-10-05T10:05:12","date_gmt":"2026-10-05T10:05:12","guid":{"rendered":"https:\/\/fivemor.com\/?p=7076741"},"modified":"2026-10-05T10:05:12","modified_gmt":"2026-10-05T10:05:12","slug":"divisor-dynamics-for-surface-fluid-simulation","status":"publish","type":"post","link":"https:\/\/fivemor.com\/?p=7076741","title":{"rendered":"Divisor Dynamics for Surface Fluid Simulation"},"content":{"rendered":"<p> <br \/>\n<\/p>\n<div id=\"post-4612\">\n<p>\t\t\t\t\t<!-- .entry-meta --><\/p>\n<div class=\"entry-content\">\n<p class=\"wp-block-paragraph\">Rudresh Veerkhare, Hang Yin, Albert Chern<\/p>\n<p class=\"wp-block-paragraph\">We introduce a simulation method for point vortices on surfaces with arbitrary topology. We show that incorporating the dynamics of the harmonic components on a non-simply-connected surface is equivalent to introducing a new fluid invariant that is conserved over time. This invariant admits an elegant formulation in terms of the divisor class of point vortices, viewed as a divisor on a Riemann surface. To clarify this connection, we establish a nontrivial bridge between fluid dynamics and the theory of divisors in algebraic geometry. By exploiting this invariant, our simulation method becomes a simple modification of the vortex particle-on-mesh method, which extends its applicability to surfaces with arbitrary topology.<\/p>\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/rudresh.net\/publications\/divisor-dynamics\/\">Divisor Dynamics for Surface Fluid Simulation<\/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\/10\/02\/divisor-dynamics-for-surface-fluid-simulation\/\" title=\"Permalink to Divisor Dynamics for Surface Fluid Simulation\" 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>Rudresh Veerkhare, Hang Yin, Albert Chern We introduce a simulation method for point vortices on surfaces with arbitrary topology. We show that incorporating the dynamics of the harmonic components on a non-simply-connected surface is equivalent to introducing a new fluid invariant that is conserved over time. This invariant admits an elegant formulation in terms of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":7070236,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12035],"tags":[237181,11538,3081,6283,6279],"dealstore":[],"offerexpiration":[],"class_list":["post-7076741","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-animation","tag-divisor","tag-dynamics","tag-fluid","tag-simulation","tag-surface"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Divisor Dynamics for Surface Fluid Simulation - 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=7076741\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Divisor Dynamics for Surface Fluid Simulation - Som2ny Network\" \/>\n<meta property=\"og:description\" content=\"Rudresh Veerkhare, Hang Yin, Albert Chern We introduce a simulation method for point vortices on surfaces with arbitrary topology. We show that incorporating the dynamics of the harmonic components on a non-simply-connected surface is equivalent to introducing a new fluid invariant that is conserved over time. This invariant admits an elegant formulation in terms of [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fivemor.com\/?p=7076741\" \/>\n<meta property=\"og:site_name\" content=\"Som2ny Network\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-05T10:05:12+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/fivemor.com\/?p=7076741#article\",\"isPartOf\":{\"@id\":\"https:\/\/fivemor.com\/?p=7076741\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371\"},\"headline\":\"Divisor Dynamics for Surface Fluid Simulation\",\"datePublished\":\"2026-10-05T10:05:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fivemor.com\/?p=7076741\"},\"wordCount\":137,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fivemor.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/?p=7076741#primaryimage\"},\"thumbnailUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg\",\"keywords\":[\"Divisor\",\"Dynamics\",\"Fluid\",\"Simulation\",\"Surface\"],\"articleSection\":[\"Animation\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fivemor.com\/?p=7076741#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fivemor.com\/?p=7076741\",\"url\":\"https:\/\/fivemor.com\/?p=7076741\",\"name\":\"Divisor Dynamics for Surface Fluid Simulation - Som2ny Network\",\"isPartOf\":{\"@id\":\"https:\/\/fivemor.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/fivemor.com\/?p=7076741#primaryimage\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/?p=7076741#primaryimage\"},\"thumbnailUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg\",\"datePublished\":\"2026-10-05T10:05:12+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/fivemor.com\/?p=7076741#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/fivemor.com\/?p=7076741\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/?p=7076741#primaryimage\",\"url\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg\",\"contentUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/fivemor.com\/?p=7076741#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/fivemor.com\/?bp_activities=1\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Divisor Dynamics for Surface Fluid Simulation\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/fivemor.com\/#website\",\"url\":\"https:\/\/fivemor.com\/\",\"name\":\"Som2ny Network\",\"description\":\"Daily Deals\",\"publisher\":{\"@id\":\"https:\/\/fivemor.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/fivemor.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/fivemor.com\/#organization\",\"name\":\"Som2ny Network\",\"url\":\"https:\/\/fivemor.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png\",\"contentUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png\",\"width\":300,\"height\":86,\"caption\":\"Som2ny Network\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png\",\"caption\":\"admin\"},\"sameAs\":[\"https:\/\/fivemor.com\"],\"url\":\"https:\/\/fivemor.com\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Divisor Dynamics for Surface Fluid Simulation - Som2ny Network","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/fivemor.com\/?p=7076741","og_locale":"en_US","og_type":"article","og_title":"Divisor Dynamics for Surface Fluid Simulation - Som2ny Network","og_description":"Rudresh Veerkhare, Hang Yin, Albert Chern We introduce a simulation method for point vortices on surfaces with arbitrary topology. We show that incorporating the dynamics of the harmonic components on a non-simply-connected surface is equivalent to introducing a new fluid invariant that is conserved over time. This invariant admits an elegant formulation in terms of [&hellip;]","og_url":"https:\/\/fivemor.com\/?p=7076741","og_site_name":"Som2ny Network","article_published_time":"2026-10-05T10:05:12+00:00","author":"admin","twitter_card":"summary_large_image","twitter_misc":{"Written by":"admin","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/fivemor.com\/?p=7076741#article","isPartOf":{"@id":"https:\/\/fivemor.com\/?p=7076741"},"author":{"name":"admin","@id":"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371"},"headline":"Divisor Dynamics for Surface Fluid Simulation","datePublished":"2026-10-05T10:05:12+00:00","mainEntityOfPage":{"@id":"https:\/\/fivemor.com\/?p=7076741"},"wordCount":137,"commentCount":0,"publisher":{"@id":"https:\/\/fivemor.com\/#organization"},"image":{"@id":"https:\/\/fivemor.com\/?p=7076741#primaryimage"},"thumbnailUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg","keywords":["Divisor","Dynamics","Fluid","Simulation","Surface"],"articleSection":["Animation"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/fivemor.com\/?p=7076741#respond"]}]},{"@type":"WebPage","@id":"https:\/\/fivemor.com\/?p=7076741","url":"https:\/\/fivemor.com\/?p=7076741","name":"Divisor Dynamics for Surface Fluid Simulation - Som2ny Network","isPartOf":{"@id":"https:\/\/fivemor.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/fivemor.com\/?p=7076741#primaryimage"},"image":{"@id":"https:\/\/fivemor.com\/?p=7076741#primaryimage"},"thumbnailUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg","datePublished":"2026-10-05T10:05:12+00:00","breadcrumb":{"@id":"https:\/\/fivemor.com\/?p=7076741#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/fivemor.com\/?p=7076741"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/?p=7076741#primaryimage","url":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg","contentUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/09\/1789535716_blank.jpg"},{"@type":"BreadcrumbList","@id":"https:\/\/fivemor.com\/?p=7076741#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/fivemor.com\/?bp_activities=1"},{"@type":"ListItem","position":2,"name":"Divisor Dynamics for Surface Fluid Simulation"}]},{"@type":"WebSite","@id":"https:\/\/fivemor.com\/#website","url":"https:\/\/fivemor.com\/","name":"Som2ny Network","description":"Daily Deals","publisher":{"@id":"https:\/\/fivemor.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/fivemor.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/fivemor.com\/#organization","name":"Som2ny Network","url":"https:\/\/fivemor.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/#\/schema\/logo\/image\/","url":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png","contentUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png","width":300,"height":86,"caption":"Som2ny Network"},"image":{"@id":"https:\/\/fivemor.com\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371","name":"admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png","caption":"admin"},"sameAs":["https:\/\/fivemor.com"],"url":"https:\/\/fivemor.com\/?author=1"}]}},"_links":{"self":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts\/7076741","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7076741"}],"version-history":[{"count":0,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts\/7076741\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/media\/7070236"}],"wp:attachment":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7076741"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7076741"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7076741"},{"taxonomy":"dealstore","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fdealstore&post=7076741"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fofferexpiration&post=7076741"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}