Obstructed gravity-driven flow down an incline

This investigation solves the problem of three-dimensional steady gravity-driven flow down an incline and around a two-dimensional cylindrical obstruction using lubrication theory. Both circular and elliptical cylindrical obstructions are considered using specific coordinates suited for the cylinder geometry. A finite difference scheme is proposed, and an asymptotic solution is derived which is used in conjunction with the numerical solution procedure. Good agreement is found with previous results for the case of the circular cylinder, and new results are obtained for the case of the elliptic cylinder.