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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 twodimensional 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
