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SUMMARYThis paper proposes a hybrid volume-of-fluid (VOF) level-set method for simulating incompressible twophase flows. Motion of the free surface is represented by a VOF algorithm that uses high resolution differencing schemes to algebraically preserve both the sharpness of interface and the boundedness of volume fraction. The VOF method is specifically based on a simple order high resolution scheme lower than that of a comparable method, but still leading to a nearly equivalent order of accuracy. Retaining the mass conservation property, the hybrid algorithm couples the proposed VOF method with a level-set distancing algorithm in an implicit manner when the normal and the curvature of the interface need to be accurate for consideration of surface tension. For practical purposes, it is developed to be efficiently and easily extensible to three-dimensional applications with a minor implementation complexity. The accuracy and convergence properties of the method are verified through a wide range of tests: advection of rigid interfaces of different shapes, a three-dimensional air bubble's rising in viscous liquids, a two-dimensional dam-break, and a three-dimensional dam-break over an obstacle mounted on the bottom of a tank. The standard advection tests show that the volume advection algorithm is comparable in accuracy with geometric interface reconstruction algorithms of higher accuracy than other interface capturing-based methods found in the literature. The numerical results for the remainder of tests show a good agreement with other numerical solutions or available experimental data.

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SUMMARYTo enhance the applicability of CFD techniques to the hull form design of modern commercial ships, an e cient and robust numerical method for turbulent ow calculation is developed. The preprocessor is composed of hull form presentation, surface mesh generation, and ÿeld grid generation. The ÿnite-volume method is utilised to solve the Reynolds-averaged Navier-Stokes equations. Three k-turbulence models, i.e., the standard k-model (SKE), the RNG-based k-model (RNG), and the realisable kmodel (RKE), are evaluated to investigate the di erence caused by the turbulence model. The developed numerical method is applied to two practical VLCC hull forms with the same forebody and the slightly di erent afterbodies in order to ÿnd out whether CFD can capture the di erence of stern ow due to hull form variation. It is found that RKE successfully predict the strength and location of bilge vortex, while SKE and RNG fail. However, all three models can provide the right information on the nominal wake di erence between two hull forms.