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

摘要

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.