A 3-D time-domain numerical coupled model for nonlinear waves acting on a ship in a harbor has been developed in the present study. The whole domain is divided into the inner domain and the outer domain. The inner domain is the area around the ship, where the flow is expressed by the Laplace equation and numerically solved by the finite element method. The other area is the outer domain, where the flow is described by the higher-order Boussinesq equations and numerically solved by the finite difference method. The matching conditions on the interfaces between the inner domain and the outer domain, the procedure of coupled solution, the length of common domain and the mesh generation in the inner domain are discussed in detail. The other coupled model with the flow in the inner domain governed by the simplified linear Euler equations and relevant physical experiment are adopted to validate the present coupled model, and it is shown that the numerical results of the present model agree with the experimental data, so the present model can be used for the study on the effect of nonlinear waves acting on a fixed ship in a large area and provide a reference for the time-domain simulation of nonlinear wave forces on an arbitrary object in a large harbor and the 3-D district computation in the future. 3-D coupled model, nonlinear waves, boussinesq equations, laplace equationFor harbor engineering, it is often concerned with the calculations of nonlinear wave forces on a ship moored in a harbor. In this case, the wave motions in almost the total harbor area should be taken into consideration because the waves in the harbor will undergo reflections from the harbor boundaries and refractions on the varying bottom of the harbor. Since the nonlinearity of water

No abstract

Flows around tandem square cylinders at Re = 100 are numerically studied using a characteristic-based penalty operator splitting finite element method based on a multistep algorithm. The validation of the code and numerical method is performed for flows around single square cylinders. L/D effects (with L being the center-to-center distance and D being the square cylinder width) on the flow structures and parameters are investigated for 1.5 ≤ L/D ≤ 9.0. The flow structures, especially far downstream of the square cylinder, indicate six distinct flow regimes. The two-layered vortex formation (TVF) and secondary vortices formation (SVF) modes are defined, and their mechanisms are analyzed. The evolution of TVF into SVF proceeds through the combination of single and binary vortex formations. Variations in the physical flow parameters, including the coefficients of fluctuating lift (CL′), time-averaged drag (C̄D), and amplitude lift (CLA), as well as the Strouhal number and phase lag (ϕ), are analyzed for various L/D values. Obvious jumps in the flow parameters occur at both square cylinders for L/D = 4.4–4.5 because of vortex impingement. Finally, insight into the physics underlying the relationship between CL−upA, CL−up′, and ϕ is derived from the simulation results. The local maximum and minimum of CL−upA and CL−up′ occur at ϕ = 2π and 3π, respectively, corresponding to in-phase and anti-phase vortex shedding by the cylinders. The pressures on the upper and lower sides of the upstream square cylinder decrease and increase, respectively, leading to reductions in CL−upA and CL−up′ as the flow pattern changes from in-phase to anti-phase.

No abstract