Semi-Implicit Schemes For Free Surface Flow Simulation

Abstract

This paper present two-dimensional numerical simulation of free surface flows by
semi-implicit projection method. The semi-implicit schemes are studied with the purpose of
introducing them into the GENSMAC method. The viscous terms are treated by Backward Implicit
and Crank-Nicolson methods, and the non-linear convection terms are, explicitly, approximated
by the high order upwind VONOS (Variable-Order Non-oscillatory Scheme) scheme. The
boundary conditions for the pressure field at the free surface are treated implicitly, and for the
velocity field explicitly. The numerical method is then applied to the simulation of free surface
and confined flows, and the numerical results show that the present technique eliminates the
stability restriction in the original explicit method.