A numerical method for the analysis of flexible bodies in unsteady viscous flows

Abstract

A two-dimensional numerical model for unsteady viscous flow around flexible bodies is developed. Bodies are represented by distributed body forces. The body force density is found at every time-step so as to adjust the velocity within the computational cells occupied by the body to a prescribed value. The method combines certain ideas from the immersed boundary method and the volume of fluid method. The main advantage of this method is that the computations can be effected on a Cartesian grid, without having to fit the grid to the body surface. This is particularly useful in the case of flexible bodies, in which case the surface of the object changes dynamically, and in the case of multiple bodies moving relatively to each other. The capabilities of the model are demonstrated through the study of the flow around a flapping flexible airfoil. The novelty of this method is that the surface of the airfoil is modelled as an active flexible skin that actually drives the flow. The accuracy and fidelity of the model are validated by reproducing well-established results for vortex shedding from a stationary as well as oscillating rigid cylinder. Copyright © 2006 John Wiley & Sons, Ltd.