An Implicit Finite Difference Method for Thin Film Flow

Thin film flow on an inclined plane can be modeled from lubrication theory. Together with boundary conditions, the governing equations can be formulated into a single equation of the thickness of the fluid, and solved numerically by an implicit finite difference method. In analyzing the equation, the linearized equation is considered here, to see the characteristic of the solution as wave propagation and the effect of the physical parameter. We found that the wave propagates by reducing the amplitude, and the wave speed is affected by the steepness of the plane. All of these can be indicated in the linearized equation. Numerical wave-simulation is presented in this paper.