A turbulent combustion subgrid model, inspired by the Linear Eddy Model for Large Eddy Simulation (LEM-LES), is developed to study highly compressible and reactive flows involving very rapid transients in pressure and energy. The model is intended to be a one-dimensional treatment of a diffusion-reaction system within a multi-dimensional LES cell. The goal is to reduce the expense of solving a complete multi-dimensional problem through Direct Numerical Simulation (DNS) while preserving micro-scale hotspots and their physical effects on ignition. The current approach features a Lagrangian description of fluid particles on the subgrid for increased accuracy. Recently, the model approach has been verified for various fundamental 1-D test cases, including inert mixing, constant volume ignition, shock tube problems and laminar flame propagation. In the current study, the model is extended to treat turbulent methane-air flames in one-dimension. Also, a 1-D piston-driven laminar shock flame interaction and its subsequent transition to detonation is modelled. Results confirm that both laminar and turbulent flame speeds are reproduced when compared against 1D computations of the Navier Stokes equations (1D-NS) and experiments, respectively. Furthermore, the model offers a good prediction for detonation initiation in the presence of shock waves when compared to high and low-resolution 1D-NS simulations. Finally, the model is demonstrated to reproduce the correct detonation structures, velocities, and instability behaviour when compared to theory and the 1D-NS computations. (C) 2015 Elsevier Ltd. All rights reserved.