The largest hydrogen-air explosion in the open atmosphere is analysed using large eddy simulation (LES) with two combustion models. The first model is based on the analysis of flame front self-induced turbulence by Karlovitz with a maximum augmentation of the stoichiometric hydrogen-air burning velocity of 3.6. Flame front wrinkling due to flow turbulence is modelled using a combustion model based on the renormalization group theory. The second approach uses fractal theory and increases the burning rate with radius as R-1/3. The first model provided a nearly constant flame velocity after initial acceleration, contradictory to theory and experiments. The second model provided better agreement with experiment on flame radius and acceleration, but overestimated the pressure wave peak in the positive phase. Analysis of the results demonstrates that the theoretical value of the fractal dimension D = 2.33 in the simulations could be reduced, particularly due to partial resolution of flame front wrinkling by LES.