A Rapid Boundary-Element Method for Modeling Viscous Flow Within Asymptotically-Thin Gaps

Abstract

A new boundary-element method is presented for the rapid and accurate solution of viscous-flow boundary-value problems in which the inherent geometry has a high aspect ratio, R ≫ 1, As such, the method is particularly suited to the investigation of steady flow within thin-gap bearings of arbitrary geometry, in which the spatial dimension in one direction is an order of magnitude greater than that in a perpendicular direction. Our theory predicts that the new method is O (R 2 ) times faster than, and requires O (R −1 ) the storage of, existing boundary-element techniques with equivalent computational mesh resolution. The new method is applied to the test problem of steady 2-D viscous flow within an exponential-profile slider bearing, and results obtained provide convincing evidence to support the theory in that, as R → ∞, the thin-film solution is recovered. The new method, which brings problems which were hitherto computationally restrictive within reach of modest computational platforms, is intended to provide the basis of a fast and accurate solver which can incorporate random surface roughness.