An Eulerian Monte-Carlo approach, the so-called Eulerian stochastic fields (ESF) method is implemented and evaluated for simulation of non-premixed hydrogen/air combustion in supersonic flows. The ESF method is integrated into a compressible flow large eddy simulation (LES) solver, and validated on a supersonic combustor with a strut as flame holder. Comparison with experimental data and with results from a well-stirred reactor (WSR) model demonstrates the advantage of the LES-ESF method for simulation of local extinction and re-ignition phenomena. The hydrogen/air flame structure and the stabilization of the combustion process in the supersonic combustor are analysed based on the present LES-ESF method. Oscillation of the recirculation zones is found to be the dominant mechanism for the local-extinction/re-ignition and the flame stabilization under the present condition. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.