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 suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.

翻译：这项工作涉及在流体结构互动(FSI)中应用几何精确波束理论所产生的研究问题。 几何精确波束理论已证明是一种计算效率高的方法,可以模拟滑体结构的行为,同时导致相当精密的问题描述。 特别是,我们建议采用混合维嵌入的有限元素方法,将一维精确波束方程式与三维背景流体网状组合在一起,称为流波束相互作用(FBI),比照FSI的既定概念。在这里,流体被牛顿流体不可压缩的低热流纳维埃-斯托克斯方程式所描述。特别是,我们介绍了由此产生的单向组合办法的解决方案的算法方面,并通过选定的数字实例,分析其是否合适,不仅作为独立的方法,而且作为整个双向组合办法的扩展。