An explicit method for the nonlinear interaction between water waves and variable and moving bottom topography

A fully nonlinear and fully dispersive method for the interaction between free surface waves and a variable bottom topography in space and time in three dimensions is derived. A Green function potential formulation expresses the normal velocity of the free surface in terms of the bathymetry and its motion. An explicit, fast version of the method is derived in Fourier space with evaluations using FFT. Practice shows that the explicit method captures the most essential parts of the wave field. This leads to a time-integration that is very accurate and orders of magnitude faster than existing full potential formulation methods. Fully resolved simulations of the nonlinear and dispersive wave fields are enabled from the generation to the shoaling of the waves, including the onshore flow which is handled by suitable numerical beaches.