# Two-Dimensional Free-Surface Flow Modeling for Wave-Structure Interactions and Induced Motions of Floating Bodies

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Department of Maritime Information and Technology, National Kaohsiung University of Science and Technology, Kaohsiung City 80543, Taiwan

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Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77004, USA

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Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung City 20224, Taiwan

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Author to whom correspondence should be addressed.

Received: 31 December 2019 / Revised: 11 February 2020 / Accepted: 12 February 2020 / Published: 15 February 2020

(This article belongs to the Special Issue Interaction between Waves and Maritime Structures)

In this study, the level set (LS) and immersed boundary (IB) methods were integrated into a Navier–Stokes equation two-phase flow solver, to investigate wave-structure interactions and induced motions of floating bodies in two dimensions. The movement of an interfacial boundary of two fluids, even with severe free-surface deformation, is tracked by using the level set method, while an immersed object inside a fluid domain is treated by the IB method. Both approaches can be implemented by solving the Navier–Stokes equations for viscous laminar flows with embedded objects in fluids. For accurate treatment of the solid–liquid phase, appropriate source terms as forcing functions to take into account the hydrodynamic effects on the body boundaries are added into the governing equations. The integrated compact interfacial tracking techniques between the interfaces of gas–liquid phase and the solid–liquid phase allow the use of a combined Eulerian Cartesian and Lagrangian grid system. Problems related to the fluid-structure interactions and induced motions of a floating body, such as (a) a dam-break wave over a dry bed; (b) a dam-break wave over either a submerged semicircular or rectangular cylinder; (c) wave decomposition process over a trapezoid breakwater; (d) a free-falling wedge into a water body; and (e) wave packet interacting with a floating body are selected to test the model performance. For all cases, the computed results are found to agree reasonably well with published experimental data and numerical solutions. For the case of modeling wave decomposition process, improved solutions are obtained. The detailed features of flow phenomena described by the physical variables of velocity, pressure and vorticity are presented and discussed. The present two-phase flow model is proved to have the advantage of simulating the cases with induced severe interfacial oscillations and coupled gas (or air) motions where the single-phase model may miss the contributions of the air motions on the interfaces. Additionally, the proposed method with uses of the LS and IB methods is demonstrated to be able to achieve the reliable predictions of complex flow fields.