  We present preliminary result for the step-scaling study of the coupling
constant with the Yang-Mills gradient flow, in the twelve-favour SU(3) gauge
theory. In this work, the lattice simulation is performed using unimproved
staggered fermions and the Wilson plaquette gauge action, from which the
gradient flow is also implemented. Imposing twisted boundary condition a'la
t'Hooft and Parisi, our calculation is performed at zero fermion mass. The
renormalised coupling constant is extracted via the computation of the energy
density. In order to examine the reliability of the continuum extrapolation, we
investigate this coupling constant using two different lattice discretisations.
Our result shows that in order to control the systematic effects in the
continuum extrapolation, it is necessary to implement a large enough
gradient-flow time. In the current calculation, the gauge-field averaging
radius corresponding to the flow time has to be as large as 40% of the lattice
size.
