Fluid structure interaction with low and high order flexibility using volume penalization

We present a new numerical scheme for the simulation of deformable objects immersed in a viscous incompressible fluid. The two-dimensional Navier--Stokes equations are discretized with an efficient Fourier pseudo-spectral scheme. Using the volume penalization method arbitrary inflow conditions can be enforced, together with the no-slip conditions at the boundary of the immersed solid object. The code is validated using classical fluid-structure interaction benchmarks, a channel flow with an immersed cylinder and attached flexible foil. We make a comparison between numerical simulations of deformable foils of two different types. The first consists of two rigid plates linked with a torsion spring (low-order flexibility). The second is a flexible plate modeled using a non-linear beam equation (high-order flexibility). We also compare these results with numerical simulations and experiments carried out by Toomey and Eldredge (Phys. Fluids 20, 073603, 2008).