Immersed boundary simulations of fluid shear-induced deformation of a cantilever beam

We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary method has been employed to simulate numerically the fluid-structure interaction problem. We investigate how variations in physical and numerical parameters change the effective material properties of the elastic beam and compare the results qualitatively with linear beam theory. We also pay careful attention to "corner effects" -- irregularities in beam shape near the free and fixed ends -- and show how this can be remedied by smoothing out the corners with a "fillet" or rounded shape. Finally, we extend the immersed boundary formulation to include porosity in the beam and investigate the effect that the resultant porous flow has on beam deflection.