Implicit Numerical Algorithm on Curvilinear Coordinates for Simulation of Free-Surface Flows

Document Type : Research Article

Authors

Abstract

Numerical solution of flows with a freely moving boundary is of great importance in practical
application such as ship hydrodynamics. Details are given of the development of a two-dimensional
vertical numerical model for simulating unsteady and steady free-surface flows on a non-staggered
grid in curvilinear coordinates, using a non-hydrostatic pressure distribution. In this model, Reynolds
equation and the kinematic free-surface boundary condition are solved simultaneously, so that the
water surface elevation can be integrated into the solution and solved for, together with the velocity
and pressure field. In the computational space, the Cartesian velocity components and the pressure are
defined at the center of a control volume, while the volume fluxes are defined at the mid-point on their
corresponding cell faces. Detailed numerical results are presented for the wave generation above an
obstacle and small amplitude Stokes waves. The results show that the numerical algorithm described is
able to produce accurate predictions and is also easy to apply.