Comparison of numerical methods for 3D Fluid-Structure Interaction problems at low Reynolds numbers

The objective of this work is to compare two numerical methods to solve 3D FSI problems for flexible bodies. In both methods, the fluid phase is computed with the in-house code TUCAN, that solves the Navier-Stokes equations of the incompressible flow, where the presence of the body is modelled by using the Immersed Boundary Method proposed by Uhlmann (2005; J. Comp. Phys. 209). For the structural solver, the first method uses a multi-body algorithm (MB) based on the rigid-body dynamics algorithm proposed by Felis (2017; Auton. Robot. 41), modelling the flexibility of the body as a system of rigid bodies connected by flexible joints (i.e, springs). The second method employs an in-house, non-linear, finite-element structural solver (AUGUSTO) to model the flexibility of the body. Time-integration is performed using a $\beta$-Newmark method with numerical damping on high-order modal spurious artifacts. The coupling between the fluid solver (TUCAN) and the structural solver (MB or AUGUSTO) is weak in both cases. Results will be presented for a flexible plate ($\pi_0 = O(10^0-10^2), \pi_1 = O(10^{-4} - 10^{-2})$) immersed on a free stream ($Re = O(100)$), allowing a direct comparison between both structural solvers.