As current densities in alkaline water electrolysers increase, the resistive losses become increasingly important due to the locally high gas fraction around the electrodes, even in zero-gap configurations. Nonetheless, quantitative measurement of the distribution of these high gas fractions is difficult. Consequently, a numerical approach is useful to assess the impact of bubbles on electrolysis. However, models that couple current density and gas fraction distributions in a non-trivial geometry are currently lacking. We show that typically used models in the literature predict unrealistically high gas fractions in electrode-resolved simulations. To improve this, we added to the mixture model equations a solid pressure model similar to that used in simulations of dense granular flows. With the addition of this model, two-dimensional simulations of a lab-scale electrolysis cell accurately reproduce previously reported experimental results. This allows, for the first time, to predict local overpotentials influenced by the bubble distribution, opening the way towards computational optimisation of the electrode geometry.