The present article proposes a partitioned Dirichlet-Neumann algorithm, that allows to address unique challenges arising from a novel mixed-dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar finite element type discretization. Here, the fibers are modeled via one-dimensional (1D) partial differential equations based on geometrically exact nonlinear beam theory, while the flow is described by the three-dimensional (3D) incompressible Navier-Stokes equations. The arising truly mixed-dimensional 1D-3D coupling scheme constitutes a novel numerical strategy, that naturally necessitates specifically tailored algorithmic solution schemes to ensure an accurate and efficient computational treatment. In particular, we present a strongly coupled partitioned solution algorithm based on a Quasi-Newton method for applications involving fibers with high slenderness ratios that usually present a challenge with regard to the well-known added mass effect. The influence of all employed algorithmic and numerical parameters, namely the applied acceleration technique, the employed constraint regularization parameter as well as shape functions, on efficiency and results of the solution procedure is studied through appropriate examples. Finally, the convergence of the two-way coupled mixed-dimensional problem solution under uniform mesh refinement is demonstrated, and the method's capabilities in capturing flow phenomena at large geometric scale separation is illustrated by the example of a submersed vegetation canopy.

翻译：本文提出了一种分区的Dirichlet-Neumann算法，用于解决通过正则化mortar有限元类型离散化将极细纤维嵌入流体流动时，由新型混合维度耦合带来的独特挑战。其中，纤维基于几何精确非线性梁理论通过一维偏微分方程建模，而流动由三维不可压缩Navier-Stokes方程描述。所提出的真正混合维度的一维-三维耦合方案构成了一种新颖的数值策略，自然需要专门定制的算法求解方案以确保准确且高效的计算处理。特别地，我们针对具有高长细比的纤维（这类纤维通常因著名的附加质量效应而带来挑战）的应用，提出了一种基于拟牛顿法的强耦合分区求解算法。通过适当的算例，研究了所有采用的算法和数值参数（即加速技术、约束正则化参数以及形函数）对求解过程效率和结果的影响。最后，展示了在均匀网格细化下双向耦合混合维度问题解的收敛性，并通过淹没植被冠层的算例说明了该方法在捕捉大几何尺度分离下的流动现象方面的能力。