A numerical method has been developed to compute the viscous ship flow on non-orthogonal curvilinear grids. The single-phase level set method is adopted to capture the free surface, and an eigenvaluebased pseudo-compressibility finite difference method is used to solve the fully-coupled pressure and velocity equations. In this method, the pressure-velocity system is only solved in the water region. The pressure and velocity are extended from the free surface into the air region along the direction of the level set gradients by enforcing the free surface interfacial jump conditions. The turbulence equations are decoupled from the pressure-velocity system but are solved in a similar way by extending the values of the values at the free surface into the air. The level set function is calculated using a simple transport equation followed by a non-conservative reinitialization step. Both steps are decoupled from the pressure-velocity and turbulence equations. The deferred-correction approach is used for all the equations to achieve high-order precision for the convection terms and to minimize the computational cost. Validations have been carried out for the free surface flows around a Wigley hull and a surface combatant model, DTMB 5512. The numerical results are in good agreement with the experimental data.


Computational fluid dynamics (CFD) has been widely used to predict ship resistance. The methods used for simulating viscous free surface flow can be grouped in two main classes: surface tracking and surface capturing. In a surface tracking method, the grid is moved to determine the configuration of the free surface at next time step. Surface capturing methods solve the flow on a fixed Eulerian grid and use an auxiliary equation to determine the profile of the free surface. Surface tracking methods are limited by their ability to deal with distorted or breaking waves.

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