An improved VOF method with anti-ventilation techniques for the hydrodynamic assessment of planing hulls-Part 1: Theory

Abstract

The numerical prediction of the hydrodynamic characteristics for planing hulls has always been challenging due to numerical ventilation (NV), which is the unphysical entrainment of air under a hull. The capture of the wetted surface, the pressure distribution, the spray, and wave-making phenomena may suffer from this. In this paper series, the characteristics of the NV were analyzed, and anti-ventilation techniques based on the volume of fluid (VOF) method were developed and applied. The NV was formed by the unphysically transported air phase in the wetted surface. To counteract the unphysical transport, pseudo diffusive fluxes in specific directions were introduced by adding an artificial diffusion term to the VOF equation for the pressure area (PA). The unphysical results caused by other numerical issues could also be dissipated by this term. The boundness of the underlying discretization scheme for the modified VOF equation was proved by stability analysis. Based on the anti-ventilation techniques, a novel systematic procedure for the hydrodynamic assessment of planing hulls was developed to improve the accuracy, stability, and convergence rate. Part 1 of this paper series contains the details of the NV and the theory of the anti-ventilation techniques. Part 2 provides the application and validation cases.