  A collection of arbitrarily-shaped solid objects, each moving at a constant
speed, can be used to mix or stir ideal fluid, and can give rise to interesting
flow patterns. Assuming these systems of fluid stirrers are two-dimensional,
the mathematical problem of resolving the flow field - given a particular
distribution of any finite number of stirrers of specified shape and speed -
can be formulated as a Riemann-Hilbert problem. We show that this
Riemann-Hilbert problem can be solved numerically using a fast and accurate
algorithm for any finite number of stirrers based around a boundary integral
equation with the generalized Neumann kernel. Various systems of fluid stirrers
are considered, and our numerical scheme is shown to handle highly multiply
connected domains (i.e. systems of many fluid stirrers) with minimal
computational expense.
