An accurate determination of minimum ignition energy (MIE) is essential for assessing electrostatic hazards and characterising potential for occurrence of combustion in flammable mixtures. This is of utmost importance for hydrogen-air mixtures characterised by a MIE equal to 0.017 mJ, whereas conventional flammable gases are characterised by MIE typically higher than 0.1 mJ. The study aims at developing and validating a CFD three-dimensional model capable to simulate complex unsteady physical and chemical phenomena underlying capacitive discharge spark. The model accounts for the experimental apparatus details, including the effect of electrodes' gap and associated heat losses. The numerical approach accurately reproduced the experimental measurements of MIE for mixtures of hydrogen with air at initial temperature ranging from ambient (T = 288 K) to cryogenic (T = 123 K). Hydrogen concentration in air was included in the range 10–55% for tests at T = 288 K, and 20–60% for tests at T = 173 K and 123 K respectively. Simulations assess the impact of experimental characteristics and design, such as the electrodes’ dimension, and numerical features on process dynamics, growth of the flame kernel and MIE predictions.