Numerical modeling of three-dimensional water waves and their interaction with structures

Abstract

A three-dimensional NumErical Wave TANK (NEWTANK) has been developed to study water waves and wave-structure interaction. The numerical model solves the incompressible spatially averaged Navier-Stokes (SANS) equations for the two-phase flow. The large-eddy-simulation (LES) approach is adopted to model the turbulence dissipation using the Smagorinsky sub-grid scale (SGS) closure. The two-step projection method is employed in the numerical solutions, aided by a Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate volume-of-fluid (VOF) method, which is very efficient and robust, is used track the highly distorted and broken free surface. A virtual boundary force (VBF) method is proposed to simulate the structure of complex shape instead of applying the conventional boundary condition around the structure. When a moving tank under 6 degree-of-freedom (D.O.F.) of motion is simulated, it will be constructed on the non-inertial reference frame to avoid applying the complicated boundary condition.The numerical model is first used to study free liquid sloshing in a confined tank, including both 2-D and 3-D cases. The numerical results compare very well with the linear analytical solution, Boussinesq results and the results calculated by other NSE solver. The model is then employed to study forced liquid sloshing in an excited tank. For 2-D surge excitation, the numerical results of linear motion are compared with the analytical solution while the results of nonlinear motion are compared with the experimental data for free surface displacements. Good agreements are obtained. Further studies are investigated on 3-D liquid sloshing. A linear analytical solution is proposed for 3-D liquid sloshing under combined surge and sway excitations. The model is validated by comparing the numerical results with the linear analytical solution, experimental data and other numerical solutions. Finally, a demonstration of violent liquid sloshing under 6 D.O.F. of motion with broken free surface in a 3-D tank, which has not been investigated before, is presented and discussed.Further investigations on wave-structure interactions are attempted and discussed. The proposed VBF approach is employed to model surface-piercing structures. The VBF method is first used to simulate a nonbreaking solitary wave runup and rundown on a 2-D steep slope. The numerical results compare very well with experimental data in terms of both free surface displacements and velocities. The model is then adopted to study the 3-D wave diffraction by a large vertical circular cylinder. The numerical results of the present model are compared with the well-known MacCamy and Fuchs closed form analytical solution. Good agreements are obtained. Finally, the breaking wave interaction with a spar platform in deep ocean is demonstrated and discussed.