This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to model the behavior of slender structures while leading to rather well-posed problem descriptions. In particular, we propose a mixed-dimensional embedded finite element approach for the coupling of one-dimensional geometrically exact beam equations to a three-dimensional background fluid mesh, referred to as fluid–beam interaction (FBI) in analogy to the well-established notion of FSI. Here, the fluid is described by the incompressible isothermal Navier–Stokes equations for Newtonian fluids. In particular, we present algorithmic aspects regarding the solution of the resulting one-way coupling schemes and, through selected numerical examples, analyze their spatial convergence behavior as well as their suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.

中文翻译：

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单向耦合流体-束流相互作用：捕捉嵌入细长体对全局流体流动的影响，反之亦然

这项工作解决了在流体-结构相互作用 (FSI) 的背景下应用几何精确梁理论所产生的研究问题。几何精确梁理论已被证明是一种在计算上有效的方法来模拟细长结构的行为，同时导致相当恰当的问题描述。特别是，我们提出了一种混合维嵌入式有限元方法，用于将一维几何精确光束方程耦合到三维背景流体网格，称为流体-光束相互作用 (FBI)，类似于已建立的FSI 的概念。在这里，流体由牛顿流体的不可压缩等温 Navier-Stokes 方程描述。特别是，我们提出了关于解决所产生的单向耦合方案的算法方面，并且，