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We report some preliminary results of our ongoing non-perturbativecomputation of the twisted 't Hooft running coupling in a particular set-up,using the gradient flow to define the coupling and step scaling techniques tocompute it. For the computation we considered a pure gauge SU(3) theory in fourdimensions, defined on the lattice on an asymmetrical torus endowed withtwisted boundary conditions in a single plane, and related the energy scale ofthe coupling to an effective size combining the size of the torus and the rankof the gauge group. Additionally, we explore some of the effects of thefreezing of the topology on the computation of the coupling.

The twisted gradient flow running coupling in SU(3): a non-perturbative determination