Solving Reynolds lubrication equations using closest point projection method

In this paper we consider application of the closest point projection method to solution of Reynolds lubrication equation. The main application is thin film flow simulation in fracture during hydraulic fracturing procedure. The problems considered in the paper include model heat tranport equation, fracture flow in planar and non-planar fractures with pressure independent and pressure dependent opening. The goal of the paper is a ganeral testing of the approach for the considered class of problems.