A strongly-coupled immersed-boundary formulation for thin elastic structures

Abstract

We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with many strongly-coupled immersed-boundary methods, our method requires the solution of a nonlinear algebraic system at each time step. The system is solved through iteration, where the iterates are obtained by linearizing the system and performing a block LU factorization. This restricts all iterations to small-dimensional subsystems that scale with the number of discretization points on the immersed surface, rather than on the entire flow domain. Moreover, the iteration procedure we propose does not involve heuristic regularization parameters, and has converged in a small number of iterations for all problems we have considered. We derive our method for general deforming surfaces, and verify the method with two-dimensional test problems of geometrically nonlinear beams undergoing large amplitude flapping behavior.

Connections between resonance and nonlinearity in swimming performance of a flexible heaving plate

“…This fluid-structure coupling is enforced by the stresses on the immersed surface, and immersed-boundary methods are well known to produce spurious computations of these stresses. These unphysical stress computations were remedied by Goza et al (2016), and the techniques described therein are incorporated into the FSI algorithm of Goza & Colonius (2017) to ensure appropriate treatment of the fluid-structure coupling. The FSI solver has been validated on several flapping flag problems for flags in both the conventional configuration (pinned at the leading edge) and the inverted configuration (clamped at the trailing edge) (Goza & Colonius 2017).…”

Modeling and simulation of a fluttering cantilever in channel flow

“…In order to validate aspects of the quasi-1D model developed in section 2, we employ a two-dimensional fluid-structure algorithm (Goza & Colonius, 2017) that utilizes the immersed boundary (IB) projection method (Taira & Colonius, 2007;Colonius & Taira, 2008) along with Newton-Raphson approach to solve the strongly-coupled fluid-structure system. Strong-coupling ensures that the nonlinear constraint between the fluid and the structure is enforced at each time step, and is necessary for accurate computation of large structural deformations.…”

“…Our DNS algorithm uses an immersed-boundary projection formulation developed by Taira & Colonius in (Taira & Colonius, 2007;Colonius & Taira, 2008). The complementary FSI algorithm is a stronglycoupled formulation between the flow and the structure developed by Goza & Colonius (Goza & Colonius, 2017). Both modeling and simulations only consider two-dimensional flow, with the modeling further simplifying the problem into a quasi-1 dimensional framework.…”

Modal decomposition of fluid–structure interaction with application to flag flapping

“…The data for this analysis was obtained using the immersed-boundary method of Goza & Colonius (2017). The method allows for arbitrarily large flag displacements and rotations, and is strongly-coupled to account for the nonlinear coupling between the flag and the fluid.…”

“…The method was validated on several flapping flag problems. The physical parameters for each run are described in the subsequent subsections; see Goza & Colonius (2017) for details about the simulation parameters such as the grid spacing and time step that were used for the different simulations.…”