Non-hydrostatic Galerkin Model with Quadratic Pressure for Wave Propagation

In this work, a new two-dimensional depth-integrated non-hydrostatic model for the simulation of wave propagation using a quadratic vertical non-hydrostatic pressure profile is developed. The model is constructed by modifying an existing non-hydrostatic discontinuous/continuous Galerkin finite element model with a linear vertical non-hydrostatic pressure profile. The use of the new model in an experiment consisting of regular waves propagating over a submerged bar in a channel proved its applicability. The utilization of a weighted averaged linear/quadratic non-hydrostatic pressure profile improved the performance of the model.