  We investigate the performance of the finite volume method in solving
viscoplastic flows. The creeping square lid-driven cavity flow of a Bingham
plastic is chosen as the test case and the constitutive equation is regularised
as proposed by Papanastasiou [J. Rheol. 31 (1987) 385-404]. It is shown that
the convergence rate of the standard SIMPLE pressure-correction algorithm,
which is used to solve the algebraic equation system that is produced by the
finite volume discretisation, severely deteriorates as the Bingham number
increases, with a corresponding increase in the non-linearity of the equations.
It is shown that using the SIMPLE algorithm in a multigrid context dramatically
improves convergence, although the multigrid convergence rates are much worse
than for Newtonian flows. The numerical results obtained for Bingham numbers as
high as 1000 compare favourably with reported results of other methods.
