A sharp interface immersed boundary/VOF model coupled with wave generating and absorbing options for wave-structure interaction

In this study, a finite difference model for the viscous incompressible Navier-Stokes (N-S) equations is developed to investigate problems with respect to wave-structure interaction. A two-step projection algorithm is employed to discretize the N-S equations on a fixed Cartesian grid. Coupled with wave generating and absorbing options, the model captures free surfaces using a volume-of-fluid method with a second-order piecewise linear interface construction (PLIC-VOF). In addition, a second-order sharp interface immersed boundary (SI-IB) method is utilized to account for the no-slip boundary condition on structure surfaces. The new model is capable of simulating free surface flows and their interaction with a stationary or moving structure, and wave generating and absorbing options are available in the model for some specific cases. To validate the model from different aspects, a series of numerical experiments are conducted. These tests include an oscillating cylinder in fluid without a free surface, liquid sloshing in a tank, water exit and entry of a horizontal cylinder, some wave generation and absorption tests, and a solitary wave over a submerged rectangular obstacle. Excellent agreement is obtained when the results are compared to analytical, experimental and other numerical results. Furthermore, two cases of a submerged and a semi-submerged ellipse rotating in a tank are investigated, and some significant phenomena are observed.