Nonstaggered Boundary-fitted Coordinate Method for Free Surface Flows

A new approach based on the finite-difference technique has been developed to study the steady incompressible Navier-Stokes equations in the laminar region, where the domain is partially bounded by a free surface. The nonstaggered fractional step method is used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a numerical mapping technique. The location of the phase boundary is accomplished by means of two methods depending on the surface tension effect: the normal-stress boundary condition or the kinematic boundary condition. We have tested the accuracy and efficiency of the numerical method by solving four different test problems: lid-driven flow in an inclined cavity, film in the absence of gravity, the ‘‘stick-slip’’ problem, and the Newtonian jet swell problem.