A Boussinesq-type wave model that conserves both mass and momentum

Abstract

There are numerous ways to derive a system of 2D Boussinesq-type wave equations from the 3D potential flow equation with free-surface boundary conditions. This freedom in design is exploited here to derive a Boussinesq-type model that has a number of unique properties. It describes the depth-integrated transport of mass and momentum in strictly conservative form. Its compact formulation is independent of the vertical reference level and allows for an efficient implementation. The model is complemented with absorbing boundary conditions that dynamically take into account the average celerity and direction of both the incoming and the outgoing wave. The model is validated by means of a number of standard test cases.