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SIAM J. APPL. MATH. c 2008 Society for Industrial and Applied Mathematics
Vol. 68, No. 5, pp. 1439­1463
ASYMMETRIC CHANNEL DIVIDER IN STOKES FLOW
I. DAVID ABRAHAMS, ANTHONY M. J. DAVIS, AND
STEFAN G. LLEWELLYN SMITH
Abstract. This article examines the classic problem of Stokes flow into a divided channel with,
in contrast to previous literature, the divider barrier asymmetrically placed with respect to the
moving, parallel channel walls. The boundary value problem is reduced to a Wiener­Hopf equation
that is of matrix form and of a class for which no exact solution is known. An explicit approximate
solution, in general accurate to any specified degree, is obtained by a recent method which employs
Pad´e approximants. Numerical results exhibit the flows due to moving walls or various combinations
of downstream pressure gradients.
Key words. Stokes flow, channel flow, Wiener­Hopf technique, matrix Wiener­Hopf equations,
Pad´e approximants
AMS subject classification. 78A45
DOI. 10.1137/070703211
1. Introduction. A classic problem in two-dimensional creeping flow, having an
analogy in plane elastostatics, is the disturbance created by the presence of a semi-
infinite barrier in a channel flow (see Figure 1.1) driven by a pressure gradient and

Source: Abrahams, I. David - Department of Mathematics, University of Manchester

Collections: Mathematics