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(R2) 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.

1.
Acheson, D. J., 1990, Elementary Fluid Dynamics, Clarendon Press, Oxford.
2.
Banerjee, P. K., 1994, Boundary Element Methods In Engineering, McGraw-Hill, England.
3.
Coyle
D. J.
,
Macosko
C. W.
, and
Scriven
L. E.
,
1990
, “
The Fluid Dynamics of Reverse-Roll Coating
,”
AIChE J.
, Vol.
36
(
2
), pp.
161
174
.
4.
Decorps
S. A. M.
and
Kelmanson
M. A.
,
1997
, “
A Zonal Boundary Element Method for Analysing Heat Exchangers with Thin Extended Surfaces
,”
Computers Math. Applic.
, Vol.
33
(
8
), pp.
103
107
.
5.
Golub, G. H. and van Loan, C. F., 1989, Matrix Computations (2/e), John Hopkins University Press, Baltimore.
6.
Hansen
E. B.
,
1987
, “
Stokes Flow Down a Wall Into an Infinite Pool
,”
J. Fluid Mech.
, Vol.
178
, pp.
243
256
.
7.
Hansen
E. B.
, and
Kelmanson
M. A.
,
1994
a, “
An Integral Equation Justification of the Boundary Conditions of the Driven-Cavity Problem
,”
Int. J. Computers and Fluids
, Vol.
22
(
1
), pp.
225
240
.
8.
Hansen
E. B.
and
Kelmanson
M. A.
,
1994
b, “
Steady, Viscous, Free-Surface Flow on a Rotating Cylinder
,”
J. Fluid Mech.
, Vol.
272
, pp.
91
107
.
9.
Hashimoto
H.
and
Mongkolwongrojn
M.
,
1994
, “
Adiabatic Approximate Solution for Static and Dynamic Characteristics of Turbulent Partial Journal Bearings with Surface Roughness
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
116
(
4
), pp.
672
680
.
10.
Jaswon, M. A., and Symm, G. T., 1977, Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, London.
11.
Kelmanson
M. A.
,
1984
, “
Boundary Integral Equation Solution of Slow Flow in Arbitrarily-Shaped Bearings
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
106
(
2
), pp.
260
264
.
12.
Kelmanson
M. A.
,
1985
, “
A Consistency Analysis for the Numerical Solution of Boundary Integral Equations
,”
Appl. Num. Math.
, Vol.
1
(
5
), pp.
381
393
.
13.
Kelmanson, M. A., 1997, “A Rapid Zonal Solver for Polyelliptic PDEs in Domains with High Aspect Ratio,” Int. J. Numer. Meth. Eng., submitted.
14.
Myllerup
C. M.
and
Hamrock
B. J.
,
1994
, “
Perturbation Approach to Hydro-dynamic Lubrication Theory
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
116
(
1
), pp.
110
118
.
15.
Ockenden, H. and Ockenden, J. R., 1995, Viscous Flow, Cambridge University Press, New York.
16.
Ramesh
J.
,
Majumdar
B. C.
and
Rao
N. S.
,
1997
, “
Thermohydrodynamic Analysis of Submerged Oil Journal Bearings Considering Surface Roughness Effects
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
119
(
1
), pp.
100
106
.
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