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-type finite element discretization. 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 approximate model and numerical strategy, that naturally necessitates specifically tailored 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, a comparison to a 3D reference solution is performed, 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Dirichlet-Neumann算法，以应对通过正则化-mortar型有限元离散化将细长纤维嵌入流体流动时产生的全新混合维度耦合所特有的挑战。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，而流动则由三维不可压缩Navier-Stokes方程描述。由此产生的真正混合维度一维-三维耦合方案构成了一种新颖的近似模型和数值策略，自然需要专门定制的求解方案以确保计算过程的准确性和高效性。特别地，我们提出了一种基于拟牛顿法的强耦合分区求解算法，适用于具有高长细比的纤维应用——这类问题通常因众所周知的附加质量效应而具有挑战性。通过适当算例，研究了所有采用的算法和数值参数（即加速技术、约束正则化参数及形函数）对求解过程效率和结果的影响。最后，验证了在均匀网格细化下双向耦合混合维度问题解的收敛性，与三维参考解进行了比较，并通过淹没植被冠层实例说明了该方法在捕捉大几何尺度分离流动现象方面的能力。