Simulation of flexible filaments in a uniform flow by the immersed boundary method

An improved version of the immersed boundary (IB) method is developed for simulating flexible filaments in a uniform flow. The proposed IB method is based on an efficient Navier–Stokes solver adopting the fractional step method and a staggered Cartesian grid system. The fluid motion defined on an Eulerian grid and the filament motion defined on a Lagrangian grid are independently solved and their interaction force is explicitly calculated using a feedback law. A direct numerical method is developed to calculate the filament motion under the constraint of inextensibility. When applied to the case of a swinging filament analogous to a rope pendulum, the proposed method gave results very similar to those of the analytical solution derived using the perturbation method. For a flexible filament flapping in a uniform flow, the mechanism by which small vortex processions are produced was investigated. The bistable property of the system was observed by altering the filament length, and the effects of the boundary condition at the fixed end (simply supported or clamped) were studied. For two side-by-side filaments in a uniform flow, both in-phase flapping and out-of-phase flapping were reproduced in the present simulations. A repulsive force was included in the formulation to handle collisions between the free ends of side-by-side filaments undergoing out-of-phase flapping.