A combined volume of fluid and immersed boundary method for free surface simulations induced by solitary waves

A combined volume of fluid and immersed boundary method is developed to simulate free surface flow induced by solitary waves. The simulations of problems involving free boundaries with large deformations are known to be challenging due to the discontinuity of density and momentum flux across the interface. In order to reduce the spurious velocities and prevent unphysical tearing of the interface, an extra velocity field is designed to extend the velocity of the water into the air and to enforce a new boundary condition near the free surface. The free surface is captured using a new Volume of Fluid (VOF) method and a boundary layer is built on the air side by an immersed boundary method. A density-weight smoothing approach is used to reconstruct the velocities inside the boundary layer. The accuracy of the new solver is verified by two benchmark problems, the propagation of a solitary wave in constant depths and run-up of a solitary wave on a slope. The performances of the new solver are compared with the original VOF solver, analytical solutions and one-phase flow solver results, and better results are obtained. The simulation of a plunging wave breaking on a slope further demonstrates the capability of the new solver to capture strong air-water interactions. It is shown to improve the robustness and stability of two-phase flow simulations and higher accuracy can be obtained on a relatively coarse grid compared to the original volume of fluid method.