CoulWave (Cornell University Long and Intermediate Wave Modeling Package) was initially developed by Patrick J. Lynett and Philip L.-F. Liu. The governing equations employed in this numerical model allow for the evolution of fully nonlinear (wave amplitude to water depth ratio = O(1) ) and dispersive waves over variable bathymetry.
The numerical model uses a predictor-corrector scheme to march forward in time, and uses finite differences to approximate spatial derivatives. The model is formally accurate to fourth order both in time and in space.
More details can be found at the personal homepage of Professor Lynett at Texas A&M Univ.