Three-dimensional fluid–structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration.

A new numerical approach for modeling a class of flow-structure interaction problems typically encountered in biological systems is presented. In this approach, a previously developed, sharpinterface, immersed-boundary method for incompressible flows is used to model the fluid flow and a new, sharp-interface Cartesian grid, immersed boundary method is devised to solve the equations of linear viscoelasticity that governs the solid. The two solvers are coupled to model flow-structure interaction. This coupled solver has the advantage of simple grid generation and efficient computation on simple, single-block structured grids. The accuracy of the solid-mechanics solver is examined by applying it to a canonical problem. The solution methodology is then applied to the problem of laryngeal aerodynamics and vocal fold vibration during human phonation. This includes a threedimensional eigen analysis for a multi-layered vocal fold prototype as well as two-dimensional, flowinduced vocal fold vibration in a modeled larynx. Several salient features of the aerodynamics as well as vocal-fold dynamics are presented.

A three-dimensional computational fluid dynamics simulation is performed for a ruby-throated hummingbird (Archilochus colubris) in hovering flight. Realistic wing kinematics are adopted in the numerical model by reconstructing the wing motion from high-speed imaging data of the bird. Lift history and the three-dimensional flow pattern around the wing in full stroke cycles are captured in the simulation. Significant asymmetry is observed for lift production within a stroke cycle. In particular, the downstroke generates about 2.5 times as much vertical force as the upstroke, a result that confirms the estimate based on the measurement of the circulation in a previous experimental study. Associated with lift production is the similar power imbalance between the two half strokes. Further analysis shows that in addition to the angle of attack, wing velocity and surface area, drag-based force and wing-wake interaction also contribute significantly to the lift asymmetry. Though the wing-wake interaction could be beneficial for lift enhancement, the isolated stroke simulation shows that this benefit is buried by other opposing effects, e.g. presence of downwash. The leadingedge vortex is stable during the downstroke but may shed during the upstroke. Finally, the full-body simulation result shows that the effects of wing-wing interaction and wing-body interaction are small.

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Insect wings in flight typically deform under the combined aerodynamic force and wing inertia; whichever is dominant depends on the mass ratio defined as m ‫ء‬ = s h / ͑ f c͒, where s h is the surface density of the wing, f is the density of the air, and c is the characteristic length of the wing. To study the differences that the wing inertia makes in the aerodynamic performance of the deformable wing, a two-dimensional numerical study is applied to simulate the flow-structure interaction of a flapping wing during hovering flight. The wing section is modeled as an elastic plate, which may experience nonlinear deformations while flapping. The effect of the wing inertia on lift production, drag resistance, and power consumption is studied for a range of wing rigidity. It is found that both inertia-induced deformation and flow-induced deformation can enhance lift of the wing. However, the flow-induced deformation, which corresponds to the low-mass wing, produces less drag and leads to higher aerodynamic power efficiency. In addition, the wing deformation has a significant effect on the unsteady vortices around the wing. The implication of the findings on insect flight is discussed.