BEM solution of thin film flows on an inclined plane with a bottom outlet

This article considers the numerical analysis of thin films flowing on an inclined plane with an opening (a gap) at the bottom of the plane, representing an outlet. The film is subject to gravitational force and a constant surface shear stress at the film surface. The present problem can be regarded as a special draining-type problem, in which there is a flow bifurcation from one side of the domain (inlet flux) to the outlet and the other side of the domain. The thin film flow is modelled as governed by the two-dimensional Stokes system of equations and an investigation into the effects of surface tension, surface shear stress and geometry variation on the flow of the film into an outlet is attempted. Numerical simulations are obtained in terms of a direct boundary element method (BEM) with primitive variables of velocity and surface traction.