A two-phase flow model coupling with volume of fluid and immersed boundary methods for free surface and moving structure problems

A numerical model is developed to solve increasing ocean engineering problems involving complex and/or moving rigid structures and nonlinear free surface action with considering air movement effects. The model is based on the two-phase flow model of incompressible viscous immiscible fluids containing various interfaces, and employs a coupled immersed boundary (IB) and volume of fluid (VOF) methods. To solve the governing equations, a two-step projection method is employed and the finite difference method on a staggered and fixed Cartesian grid is used throughout the computation. The bi-conjugate gradient stabilized technique is applied to solve the pressure Poisson equation. In particular, the advection term is discretized in a composite difference scheme to enhance the stability of the algorithm. The direct forcing IB method is utilized to deal with no-slip boundary condition, while the VOF method, which employs a piecewise line interface calculation technique and a Lagrange method to reconstruct and update the interface respectively, is used to track distorted and broken free surfaces. The results of this study demonstrate the accuracy and capability of the two-phase model to simulate a moving body in free surface flows while also considering air movement effects.