{"id":5709,"date":"2022-06-10T14:40:24","date_gmt":"2022-06-10T12:40:24","guid":{"rendered":"https:\/\/www.mi.uni-koeln.de\/NumSim\/?p=5709"},"modified":"2022-06-13T09:52:21","modified_gmt":"2022-06-13T07:52:21","slug":"snapshot-chaotic-behavior-of-the-kelvin-helmholtz-instability","status":"publish","type":"post","link":"https:\/\/www.mi.uni-koeln.de\/NumSim\/2022\/06\/10\/snapshot-chaotic-behavior-of-the-kelvin-helmholtz-instability\/","title":{"rendered":"Snapshot: Chaotic behavior of the Kelvin-Helmholtz Instability"},"content":{"rendered":"<p>We investigate the Kelvin-Helmholtz instability setup of Fjordholm et al. [1], where the sharp interface in the initial condition is randomly perturbed. The simulation is done with an entropy stable DGSEM with polynomial degree N=3 and 32 x 32 grid cells. The final time is t = 2.0. Trixi.jl [2] is used with the setup found in examples\/tree_2d_dgsem\/elixir_euler_kelvin_helmholtz_instability_fjordholm_etal.jl.<\/p>\n<p>The following gif is showing 100 simulation results of the density distribution for different random interface perturbations:<\/p>\n<p><a href=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/2022\/06\/10\/snapshot-chaotic-behavior-of-the-kelvin-helmholtz-instability\/density-2\/\" rel=\"attachment wp-att-5710\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-content\/uploads\/2022\/06\/density.gif\" alt=\"\" width=\"600\" height=\"400\" class=\"aligncenter size-full wp-image-5710\" \/><\/a><\/p>\n<p>Here is the average density distribution of all 100 results:<\/p>\n<p><a href=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/2022\/06\/10\/snapshot-chaotic-behavior-of-the-kelvin-helmholtz-instability\/average\/\" rel=\"attachment wp-att-5711\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-content\/uploads\/2022\/06\/Average.png\" alt=\"\" width=\"600\" height=\"400\" class=\"aligncenter size-full wp-image-5711\" srcset=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-content\/uploads\/2022\/06\/Average.png 600w, https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-content\/uploads\/2022\/06\/Average-300x200.png 300w, https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-content\/uploads\/2022\/06\/Average-450x300.png 450w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/a><\/p>\n<p>[1] Ulrik S. Fjordholm, Roger K\u00e4ppeli, Siddhartha Mishra, Eitan Tadmor. Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws, 2014. (<a href=\"https:\/\/arxiv.org\/abs\/1402.0909\">https:\/\/arxiv.org\/abs\/1402.0909<\/a>)<br \/>\n[2] Trixi.jl, a numerical simulation framework for hyperbolic conservation laws written in Julia. (<a href=\"https:\/\/github.com\/trixi-framework\/Trixi.jl\">https:\/\/github.com\/trixi-framework\/Trixi.jl<\/a>)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We investigate the Kelvin-Helmholtz instability setup of Fjordholm et al. [1], where the sharp interface in the initial condition is randomly perturbed. The simulation is done with an entropy stable DGSEM with polynomial degree N=3 and 32 x 32 grid &hellip; <a href=\"https:\/\/www.mi.uni-koeln.de\/NumSim\/2022\/06\/10\/snapshot-chaotic-behavior-of-the-kelvin-helmholtz-instability\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts\/5709"}],"collection":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/comments?post=5709"}],"version-history":[{"count":5,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts\/5709\/revisions"}],"predecessor-version":[{"id":5716,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/posts\/5709\/revisions\/5716"}],"wp:attachment":[{"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/media?parent=5709"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/categories?post=5709"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mi.uni-koeln.de\/NumSim\/wp-json\/wp\/v2\/tags?post=5709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}