Abstract
Recently, finite-difference schemes for solving the 2-D and 3-D incompressible Navier-Stokes euations involving free surfaces have focused on improving their accuracy, stability and efficiency. The 2-D momentum equations for the contravariant velocity components and the Poisson equations for the pressure are solved by applying the SMAC like time-marching scheme, since the spurious errors and the numerical instabilities can be suppressed by employing the staggered grid and the QUICK upwind scheme in general curvilinear coordinates. Some numerical results for 2-D flows are shown to demonstrate the reliability of the present scheme.
