A fully coupled regularized mortar-type finite element approach for embedding one-dimensional fibers into three-dimensional fluid flow

TL;DR

This paper introduces a novel mixed-dimensional coupling approach using a regularized mortar finite element method to simulate slender fibers embedded in 3D fluid flow, addressing computational challenges with high slenderness ratios.

Contribution

It develops a partitioned Dirichlet-Neumann algorithm with a Quasi-Newton method for efficient, accurate simulation of 1D fibers within 3D Navier-Stokes flow, including high slenderness ratios.

Findings

Convergence demonstrated under mesh refinement

Comparison with 3D reference solution shows accuracy

Method effectively captures flow phenomena at large scale separation

Abstract

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.