Approximate Methods for Time-Dependent Gas-Film Lubrication Problems

The pressure in a thin film of gas undergoing laminar, isothermal flow is given by the so-called Reynolds equation, a nonlinear, second-order, partial differential equation of parabolic type. The Reynolds equation plays a central role in the theory of gas-film lubrication. This paper is devoted to a study of numerical procedures based upon finite differences for obtaining approximate solutions. A number of explicit, semi-explicit, and implicit difference schemes are examined from the point of view of truncation error, stability, and computational efficiency.