Shock-capturing non-hydrostatic model for fully dispersive surface wave processes

This paper describes NHWAVE, a shock-capturing non-hydrostatic model for simulating wave refraction, diffraction, shoaling, breaking and landslide-generated tsunami in finite water depth. The governing equations are the incompressible Navier–Stokes equations in conservative form, written in surface and terrain-following form using a σ coordinate. In order to apply a Godunov-type scheme, the velocities are defined at cell centers. The dynamic pressure is defined at vertically facing cell faces so that the pressure boundary condition at free surface can be precisely imposed. The HLL Riemann approximation is employed to estimate fluxes at horizontal cell faces. The nonlinear Strong Stability-Preserving (SSP) Runge–Kutta scheme is used to obtain second-order accuracy in time. The model is validated using seven test cases based on analytical solutions and experimental data. The computed results show that the model can well predict wave propagation over submerged bar, wave refraction and diffraction over an elliptical shoal as well as wave breaking, run-up and longshore current on a plane beach using relatively few (three to five) vertical layers. The model is also shown to provide accurate reproduction of a generated tsunami wave resulting from a solid translating bottom feature.