One-way coupled fluid–beam interaction: capturing the effect of embedded slender bodies on global fluid flow and vice versa

Abstract

Abstract 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 spatial convergence behavior as well as their suitability not only as stand-alone methods but also for an extension to a full two-way coupling scheme.

Keywords

• Fluid–structure interaction
• Nonlinear beam theory
• Finite element method
• Immersed boundary method
• Mixed-dimensional modeling
• 1D–3D coupling