{"id":233,"date":"2021-04-26T02:49:00","date_gmt":"2021-04-26T01:49:00","guid":{"rendered":"https:\/\/ramyrashad.com\/?p=233"},"modified":"2023-08-12T02:39:19","modified_gmt":"2023-08-12T01:39:19","slug":"navier-stokes-equations","status":"publish","type":"post","link":"https:\/\/ramyrashad.com\/index.php\/2021\/04\/26\/navier-stokes-equations\/","title":{"rendered":"Navier-Stokes Equations"},"content":{"rendered":"\n<p><strong>Research Overview<\/strong><\/p>\n\n\n\n<p>The specific aim of this work is to extend the port-Hamiltonian formulation of ideal compressible fluids (Euler equations) to Newtonian viscous fluids (Navier\u2013Stokes equations). The way this extension is developed is consistent with the core methodology of port-Hamiltonian modeling: we introduce a distributed port to interconnect the system representing ideal fluid dynamics with a purely dissipative systemthat encodes the constitutive relations peculiar of Newtonian fluids. <\/p>\n\n\n\n<p>The way to achieve the complete level of generality in this work is by extending the differential form representation of port-Hamiltonian fluid systems to tensor-valued forms and the identification of novel duality pairings that are necessary to extend the definition of power flows in this context.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Energy_Balance_Abstract-1024x572.png\" alt=\"\" class=\"wp-image-518\" width=\"682\" height=\"381\" srcset=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Energy_Balance_Abstract-1024x572.png 1024w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Energy_Balance_Abstract-300x168.png 300w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Energy_Balance_Abstract-768x429.png 768w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Energy_Balance_Abstract.png 1422w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><figcaption class=\"wp-element-caption\">Abstract energy balance for Navier\u2013Stokes equations<\/figcaption><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"520\" src=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Comp_Isen_pH_Bond_Graph.png\" alt=\"\" class=\"wp-image-519\" srcset=\"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Comp_Isen_pH_Bond_Graph.png 960w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Comp_Isen_pH_Bond_Graph-300x163.png 300w, https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/08\/Comp_Isen_pH_Bond_Graph-768x416.png 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><figcaption class=\"wp-element-caption\">Full decomposed bond graph model of the Navier\u2013Stokes equations on a general Riemannian manifold with boundary<\/figcaption><\/figure><\/div>\n\n\n<p><strong>Publications<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Ramy Rashad, Federico Califano, Andrea Brugnoli, Frederic P. Schuller, Stefano Stramigioli\u00a0(2021)\u00a0Exterior and vector calculus views of incompressible Navier-Stokes port-Hamiltonian models,\u00a0IFAC-PapersOnLine\u00a054(19),\u00a0p. 173-179,\u00a0Elsevier Ltd,\u00a0<a href=\"https:\/\/doi.org\/10.1016\/j.ifacol.2021.11.074\" target=\"_blank\" rel=\"noreferrer noopener\">doi:10.1016\/j.ifacol.2021.11.074<\/a><br><br>Federico Califano, Ramy Rashad, Frederic P. Schuller, Stefano Stramigioli\u00a0(2021)\u00a0Geometric and energy-aware decomposition of the Navier-Stokes equations: A port-Hamiltonian approach,\u00a0Physics of Fluids\u00a033(4),\u00a0AIP Publishing LLC,\u00a0<a href=\"https:\/\/doi.org\/10.1063\/5.0048359\" target=\"_blank\" rel=\"noreferrer noopener\">doi:10.1063\/5.0048359<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Ramy Rashad - Exterior and Vector Calculus Views of Incompressible Navier-Stokes Eqns - IFAC LHMNC21\" width=\"790\" height=\"444\" src=\"https:\/\/www.youtube.com\/embed\/b09cZ-UXOSY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Research Overview The specific aim of this work is to extend the port-Hamiltonian formulation of ideal compressible fluids (Euler equations) to Newtonian viscous fluids (Navier\u2013Stokes equations). The way [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":296,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"ub_ctt_via":"","_mi_skip_tracking":false,"footnotes":""},"categories":[10],"tags":[],"aioseo_notices":[],"featured_image_src":"https:\/\/ramyrashad.com\/wp-content\/uploads\/2023\/07\/NSeqns.png","author_info":{"display_name":"Ramy","author_link":"https:\/\/ramyrashad.com\/index.php\/author\/ramy-abdelmonemgmail-com\/"},"_links":{"self":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts\/233"}],"collection":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/comments?post=233"}],"version-history":[{"count":3,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts\/233\/revisions"}],"predecessor-version":[{"id":520,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/posts\/233\/revisions\/520"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/media\/296"}],"wp:attachment":[{"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/media?parent=233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/categories?post=233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ramyrashad.com\/index.php\/wp-json\/wp\/v2\/tags?post=233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}