Explosions in homogeneous reactive mixtures have been widely studied both experimentally and numerically. However, in practice, combustible mixtures are usually inhomogeneous and subject to both vertical and horizontal concentration gradients. There is still very limited understanding of the explosion characteristics in such situations. The present study aims to investigate deflagration to detonation transition (DDT) in such mixtures. Two cases in a horizontal obstructed channel with 30% and 60% blockage ratios filled with hydrogen/air mixture with vertical concentration gradients are numerically studied. These cases were experimentally investigated by Boeck et al. (2015), and hence some measurements are available for model validation. A density-based solver within the OpenFOAM CFD toolbox is developed and used. To evaluate the convective fluxes contribution, the Harten Lax van Leer Contact (HLLC) scheme is used for shock capturing. The compressible Navier-Stokes equations with a single step Arrhenius reaction are solved. The numerical results are in good qualitative and quantitative agreement with the experiments. The predictions show that the overpressure at the DDT transition stage is higher in the non-uniform mixtures than that in homogeneous mixtures under similar conditions. It is also found that increasing the blockage ratio from 30% to 60% resulted in faster flame propagation and lower propensity to DDT. The Baroclinic torque and the resulting Richtmyer Meshlcov (RM) instability are also analyzed in relation to flame acceleration and DDT. (C) 2017 Elsevier Ltd. All rights reserved.