  Roughness predominantly alters the near-wall region of turbulent flow while
the outer layer remains similar. This makes it a prime candidate for the
minimal-span channel, which only captures the near-wall flow by restricting the
spanwise channel width to be of the order of a few hundred viscous units.
Recently, Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418-431) showed
that a minimal-span channel can accurately characterise the hydraulic behaviour
of roughness. Following this, we aim to investigate the fundamental dynamics of
the minimal-span channel framework with an eye towards further improving
performance. The streamwise domain length of the channel is investigated with
the minimum length found to be three times the spanwise width or 1000 viscous
units, whichever is longer. A half-height (open) channel with slip wall is
shown to reproduce the near-wall behaviour seen in a standard channel, but with
half the number of grid points. Next, a forcing model is introduced into the
outer layer of a half-height channel to reduce the high streamwise velocity.
Finally, an investigation is conducted to see if varying the roughness Reynolds
number with time is a feasible method for obtaining the full hydraulic
behaviour of a rough surface. An empirical costing argument is developed to
determine the cost in terms of CPU hours of minimal-span channel simulations a
priori. This argument involves counting the number of eddy lifespans in the
channel, which is then related to the statistical uncertainty of the streamwise
velocity. For a given statistical uncertainty in the roughness function, this
can then be used to determine the simulation run time. Following this, a
finite-volume code with a body-fitted grid is used to determine the roughness
function for square-based pyramids using the above insights. Good agreement
with the literature for the same roughness geometry is observed.
