Coupled lubrication and Stokes flow finite elements

Abstract

A method is developed for performing a local reduction of the governing physics for fluid problems with domains that contain a combination of narrow and non-narrow regions, and the computational accuracy and performance of the method are measured. In the narrow regions of the domain, where the fluid is assumed to have no inertia and the domain height and curvature are assumed small, lubrication, or Reynolds, theory is used locally to reduce the two-dimensional Navier–Stokes equations to the one-dimensional Reynolds equation while retaining a high degree of accuracy in the overall solution. The Reynolds equation is coupled to the governing momentum and mass equations of the non-narrow region with boundary conditions on the mass and momentum flux. The localized reduction technique, termed ‘stitching,’ is demonstrated on Stokes flow for various geometries of the hydrodynamic journal bearing—a non-trivial test problem for which a known analytical solution is available. The computational advantage of the coupled Stokes–Reynolds method is illustrated on an industrially applicable fully-flooded deformable-roll coating example. The examples in this paper are limited to two-dimensional Stokes flow, but extension to three-dimensional and Navier–Stokes flow is possible. Copyright © 2003 John Wiley & Sons, Ltd.