Variational discretizations for the dynamics of fluid-conveying flexible tubes

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• 作者：Franç ; ois Gay-Balmaz^a ; ^{francois.gay-balmaz@lmd.ens.fr" class="auth_mail" title="E-mail the corresponding author} ; Vakhtang Putkaradze^b ; ^{putkarad@ualberta.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Variational integrators ; Fluid&ndash ; structure interaction ; Fluid-conveying tubes
• 刊名：Comptes Rendus Mécanique
• 出版年：2016
• 出版时间：November-December 2016
• 年：2016
• 卷：344
• 期：11-12
• 页码：769-775
• 全文大小：333 K

文摘

We derive a variational approach for discretizing fluid–structure interactions, with a particular focus on the dynamics of fluid-conveying elastic tubes. Our method is based on a discretization of the fluid's back-to-labels map and a Lie group discretization of the tube's variables, coupled with an appropriately formulated discrete version of the fluid conservation law. This approach allows the development of geometric numerical schemes for the dynamics of fluid-conveying collapsible tubes, which preserve several intrinsic geometric properties of the continuous system, such as symmetries and symplecticity. In addition, our approach can also be used to derive simplified, but geometrically consistent, low-component models for further analytical and numerical analysis of the system.