Level set immersed boundary method for coupled simulation of air/water interaction with complex floating structures

We propose a new computational approach for simulating the coupled interaction between air–water flows and arbitrarily complex floating rigid bodies. The numerical method integrates the fluid–structure interaction (FSI) curvilinear immersed boundary (CURVIB) method of Borazjani et al. (2008) [21] with a level set approach for simulating free surface flows in arbitrarily complex domains. We show that when applying the CURVIB method to simulate two-phase flow FSI problems the approach used to calculate the force imparted on the body is critical for determining the overall accuracy of the method. We develop and demonstrate the accuracy of a new approach for calculating the force, namely the pressure projection boundary condition (PPBC), which is based on projecting the pressure on the surface of the body using the momentum equation along the local normal to the body direction. Extensive numerical tests show that the new approach greatly improves the ability of the method to correctly predict the dynamics of the floating structure motion. To demonstrate the predictive capabilities of the method and its ability to simulate non-linear free surface phenomena, such as breaking waves, we apply it to various two- and three-dimensional problems involving complex rigid bodies interacting with a free surface both with prescribed body motion and coupled FSI. We show that for all cases the proposed method yields results in very good accuracy with benchmark numerical data and available experiments. The simulations also reveal the onset of dynamically rich, energetic coherent structures in the air phase induced by the waves generated as the rigid body interacts with the free surface.