Numerical simulation of breaking waves using a two-phase flow model

In this paper, a numerical two-phase flow model for incompressible viscous fluid is presented for the simulation of wave propagation in shallow water, including the processes of wave shoaling, wave breaking, wave reflection and air movement. The model consists of the continuity equation, the Navier–Stokes equations, the fractional VOF function equation, and the equations of density and viscosity. The turbulent eddy viscosity is evaluated by using the Smagorinsky's sub-grid scale model. The VOF method with an advection algorithm following [Int. J. Numer Meth. Fluids 35 (2001) 151] is employed for tracking the free surface. To solve the time evolution of the governing equations, the SMAC method and iteration technique are used. The convective terms in the momentum equation are approximated using a high accuracy CIP scheme proposed in [Comput. Phys. Commun. 66 (1991) 219]. A numerical test with dam break problem was conducted and compared with experimental data to verify the validity and stability of the model. The model was then applied to simulate the wave breaking on a sloping bottom and the numerical results were compared with experimental data. The results demonstrated that the present model is capable of simulating wave deformation in shallow water, as well as wave breaking problem.