An efficient 3D non-hydrostatic model for simulating near-shore breaking waves

This paper describes the formulation and verification of a 3D non-hydrostatic free surface water flow model with a Finite Volume Method (FVM) on unstructured grids. The model extends the Non-linear Shallow Water (NSW) equations by utilizing a non-hydrostatic pressure term for describing dispersive water waves. In order to simulate the near-shore wave dynamics, the wave breaking is modeled using a so-called splitting algorithm in the present model. When a wave is ready to break, the non-hydrostatic model is locally switched to the hydrostatic model to suppress the dispersive effects. The breaking wave front is analogy to a moving hydraulic jump, and is treated as a shock with its energy dissipation implicitly evaluated according to the shock-wave theory. The wave breaking is then simulated by solving the conventional NSW with a 2nd order Total Variation Diminishing (TVD) scheme. Extensive case studies are carried out to verify the efficiency and accuracy of the model. The numerical simulations are found to agree well with the experimental measurements.