A structured, finite-volume Euler solver for non-hydrostatic, free surface flows is developed to simulate coastal nonlinear dispersive water waves. A semi-implicit projection method which splits the pressure term into hydrostatic and non-hydrostatic parts is employed. A vertically shifted, staggered grid is designed to accommodate a new Gaussian discharge calculator and to facilitate the enforcement of a non-hydrostatic free-surface boundary condition. The Gaussian discharge calculator on the shifted grid increases the dispersion accuracy compared to traditional approaches that calculate discharges on a regular staggered grid. Numerical results are presented to demonstrate the improvements of these methods
