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SUMMARYThis paper presents the calculated results for three classes of typical modern ships in modelling of shipgenerated waves. Simulations of turbulent free-surface ows around ships are performed in a numerical water tank, based on the FINFLO-RANS SHIP solver developed at Helsinki University of Technology. The Reynolds-averaged Navier-Stokes (RANS) equations with the artiÿcial compressibility and the nonlinear free-surface boundary conditions are discretized by means of a cell-centred ÿnite-volume scheme. The convergence performance is improved with the multigrid method. A free surface is tracked using a moving mesh technology, in which the non-linear free-surface boundary conditions are given on the actual location of the free surface. Test cases recommended are a container ship, a US Navy combatant and a tanker. The calculated results are compared with the experimental data available in the literature in terms of the wave proÿles, wave pattern, and turbulent ow ÿelds for two turbulence models, Chien's low Reynolds number k-model and Baldwin-Lomax's model. Furthermore, the convergence performance, the grid reÿnement study and the e ect of turbulence models on the waves have been investigated. Additionally, comparison of two types of the dynamic free-surface boundary conditions is made.

SUMMARYThis paper describes a method for simulation of viscous flows with a free surface around realistic hull forms with a transom, which has been developed based on a FINFLO RANS solver with a moving mesh. A dry-transom model is proposed and implemented for the treatment of flows off the transom. The bulk RANS flow with the artificial compressibility is solved by a cell-centred finite volume multigrid scheme and the free surface deformed by wave motions is tracked by satisfying the kinematic and dynamic free-surface boundary conditions on the actual location of the surface. The effects of turbulence on flows are evaluated with the Baldwin-Lomax turbulence model without a wall function. A test case is modern container ship model with a transom, the Hamburg Test Case. The calculated results are validated and they agree well with the measured results in terms of the free-surface waves and the total resistance coefficient. Furthermore, the numerical solutions successfully captured many important features of the complicated interaction of the free surface with viscous flows around transom stern ships. In addition, the convergence performance and the grid refinement studies are also investigated.

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Complex single/multi-body structures are generally found in ship and ocean engineering. They have the smooth, sharp, concave, and convex surface features in common. Precise modeling of the structures is the basis of numerical simulation. However, the most widely used explicit modeling method requires considerable manual operations. The result is also difficult to reproduce. Therefore, this paper presents a Radial basis function (RBF) based hierarchical (h-) adaptive Cartesian grid method. The RBF is introduced for arbitrary implicit modeling over the Cartesian framework. Thanks to its natural properties, the RBF is easy to use, highly automated, and only needs a set of scatter points for modeling. The block-based h-adaptive mesh refinement (AMR) combined with the RBF aims to enhance the local grid resolution. It accelerates the calculation of intersecting points compared with the uniform Cartesian grid. The accuracy, efficiency, and robustness of the proposed method are validated by the simulation of the 3D analytical ellipsoidal surface and the unclosed conic surface. To select suitable parameters, we thoroughly investigated the uncertainty factors including sample points, RBF functions, and h-AMR grids. The simulation results of the single/multi-body Wigley hull and KCS hull forms verified the proper selection of the factors and the feasibility of our method to solve practical problems.