To better understand the fundamental propagation mechanism of irregular-cell (e.g., in an H2-air mixture) detonation under two RDC-relevant scenarios--propagation with (1) lateral expansion and (2) inhomogeneously mixed reactants. Three-dimensional DNS will be used to simulate H2-air detonation in a finite-thickness layer of premixed or injected non-premixed reactants bounded by a layer of hot detonation products. From the DNS, the global detonation velocity deficit and statistical data of the reaction-zone dynamics will be obtained. The detailed interplay among the mixing process, rapid shock-induced combustion, and slow diffusion-controlled combustion, will be analysed. Hydrodynamic thickness (i.e., length scale of the reaction zone driving the detonation) will be measured based on the statistical data. This information will be used to develop a theoretical model based on the ZND framework. This theoretical model will be extended to a reduced-order RDC wave-dynamics model in order to estimate the mode of wave propagation and pressure gain. This model will be validated and further improved using experimental data from other WPs.