An Euler Solver for Nonlinear Water Waves Simulation Using a Modified Staggered Grid and Gaussian Quadrature Approach

A structured finite volume Euler solver for non‐hydrostatic term, free‐surface flows has been developed to simulate nonlinear 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 the application 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.