一种将一维纤维嵌入三维流体流动的全耦合正则化mortar型有限元方法
A fully coupled regularized mortar-type finite element approach for embedding one-dimensional fibers into three-dimensional fluid flow
AI总结：
本文针对细长纤维与三维流体耦合问题，提出基于正则化mortar离散和拟牛顿强耦合分区Dirichlet-Neumann算法，验证了收敛性并展示了在浸没植被冠层流动模拟中的能力。
摘要：
本文提出了一种分区Dirichlet-Neumann算法，用于解决由正则化mortar型有限元离散将极细长纤维嵌入流体流动所引发的新型混合维耦合中的独特挑战。纤维通过基于几何精确非线性梁理论的一维（1D）偏微分方程建模，而流动则由三维（3D）不可压缩Navier-Stokes方程描述。由此产生的真正混合维1D-3D耦合方案构成了一种新型近似模型和数值策略，这自然需要专门定制的求解方案以确保准确高效的计算处理。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，用于涉及高细长比纤维的应用，这类应用通常在众所周知的附加质量效应方面存在困难。通过适当的算例研究了所有采用的算法和数值参数（即所应用的加速技术、所采用的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，展示了双向耦合混合维问题解在均匀网格细化下的收敛性，与3D参考解进行了比较，并通过浸没植被冠层的算例说明了该方法在大几何尺度分离下捕捉流动现象的能力。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
