Three-dimensional low Reynolds number flows with a free surface

Abstract

The two-dimensional leveling problem (Degani, Gutfinger, 1976) is extended to three dimensions in the case where the flow Re number is very low and attention is paid to the free surface boundary condition with surface tension effects included. The no-slip boundary condition on the wall is observed. The numerical solution falls back on the Marker and Cell (MAC) method (Harlow and Welch, 1965) with the computation region divided into a finite number of stationary rectangular cells (or boxes in the 3-D case) and fluid flow traverses the cells (or boxes).