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

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.