Coupled ghost fluid/two-phase level set method for curvilinear body-fitted grids.

*(English)*Zbl 1388.76253Summary: A coupled ghost fluid/two-phase level set method to simulate air/water turbulent flow for complex geometries using curvilinear body-fitted grids is presented. The proposed method is intended to treat ship hydrodynamics problems. The original level set method for moving interface flows was based on Heaviside functions to smooth all fluid properties across the interface. We call this the Heaviside function method (HFM). The HFM requires fine grids across the interface. The ghost fluid method (GFM) has been designed to explicitly enforce the interfacial jump conditions, but the implementation of the jump conditions in curvilinear grids is intricate. To overcome these difficulties a coupled GFM/HFM method was developed in which approximate jump conditions are derived for piezometric pressure and velocity and pressure gradients based on exact continuous velocity and stress and jump in momentum conditions with the jump in density maintained but continuity of the molecular and turbulent viscosities imposed. The implementation of the ghost points is such that no duplication of memory storage is necessary. The level set method is adopted to locate the air/water interface, and a fast marching method was implemented in curvilinear grids to reinitialize the level set function. Validations are performed for three tests: super- and sub-critical flow without wave breaking and an impulsive plunging wave breaking over 2D submerged bumps, and the flow around surface combatant model DTMB 5512. Comparisons are made against experimental data, HFM and single-phase level set computations. The proposed method performed very well and shows great potential to treat complicated turbulent flows related to ship flows.

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76F99 | Turbulence |

76T99 | Multiphase and multicomponent flows |

##### Keywords:

moving interface flows; ghost fluid method; level set method; fast marching method; curvilinear grids; ship hydrodynamics
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\textit{J. Huang} et al., Int. J. Numer. Methods Fluids 55, No. 9, 867--897 (2007; Zbl 1388.76253)

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