{"id":892,"date":"2024-04-22T21:23:03","date_gmt":"2024-04-23T04:23:03","guid":{"rendered":"\/wp\/hades\/?p=892"},"modified":"2024-04-22T21:23:03","modified_gmt":"2024-04-23T04:23:03","slug":"a-loosely-coupled-splitting-scheme-for-a-fluid-multilayered-poroelastic-structure-interaction-problem","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/04\/22\/a-loosely-coupled-splitting-scheme-for-a-fluid-multilayered-poroelastic-structure-interaction-problem\/","title":{"rendered":"A loosely coupled splitting scheme for a fluid &#8211; multilayered poroelastic structure interaction problem"},"content":{"rendered":"\n\t\t\t\t\n<p>The HADES seminar on Tuesday,&nbsp;<strong>April 23rd<\/strong>, will be at <strong>3:30pm<\/strong>&nbsp;in&nbsp;<strong>Room 939.<\/strong><\/p>\n\n\n\n<p><strong>Speaker<\/strong>: <a href=\"https:\/\/math.berkeley.edu\/~als\/\">Andrew Scharf<\/a><\/p>\n\n\n\n<p><strong>Abstract:<\/strong> Multilayered poroelastic structures are found in many biological  tissues, such as cartilage and the cornea, and find use in the design of  bioartificial organs and other bioengineering applications. Motivated  by these applications, we analyze the interaction of a free fluid flow  modeled by the time-dependent Stokes equation and a multilayered  poroelastic structure consisting of a thick Biot layer and a thin,  linear, poroelastic membrane separating it from the Stokes flow. The  resulting equations are linearly coupled across the thin structure  domain through physical coupling conditions such as the  Beavers-Joseph-Saffman condition. I will discuss previous work in  which weak solutions were shown to exist by constructing approximate  solutions using Rothe&#8217;s method. While a number of partitioned numerical  schemes have been developed for the interaction of Stokes flow with a  thick Biot structure, the existence of an additional thin poroelastic  plate in the model presents new challenges related to finite element  analysis on multiscale domains. As an important step toward an efficient  numerical scheme for this model, we develop a novel, fully discrete  partitioned method for the multilayered poroelastic structure problem  based on the fixed strain Biot splitting method. This work is carried  out jointly with Sun\u010dica \u010cani\u0107 and Jeffrey Kuan at the  University of California, Berkeley and Martina Buka\u010d at the  University of Notre Dame.<\/p>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,&nbsp;April 23rd, will be at 3:30pm&nbsp;in&nbsp;Room 939. Speaker: Andrew Scharf Abstract: Multilayered poroelastic structures are found in many biological tissues, such as cartilage and the cornea, and find use in the design of bioartificial organs and other bioengineering applications. Motivated by these applications, we analyze the interaction of a free fluid [&hellip;]<\/p>\n","protected":false},"author":92,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-892","post","type-post","status-publish","format-standard","hentry","category-spring-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/92"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=892"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/892\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}