Book excerpt: Detonation in gaseous mixtures is a phenomenon of great importance for explosion safety assessment in hydrogen economy and for the development of advanced detonation-based propulsion systems. In practical applications, a detonation is generally caused by a deflagration to detonation transition (DDT) since a smaller amount of energy is required compared to a direct initiation. The key issue of DDT is finding the appropriate mechanisms to rapidly generate the detonation waves with a relatively weak ignition source. The objective of this work is to study numerically the possibility of DDT resulting from shock-multiple cylindrical flames interaction. The numerical setup aims to mimic an array of laminar flames ignited at different spark times, artificially inducing chemical activity to stimulate the coupling between the gasdynamics and the chemical energy release for the transition of deflagration-to-detonation. Using numerical simulations, a number of physical parameters are varied to determine their effect on the run-up distance as well as the time until the onset of detonation occurs, and to explore any scaling relationship among different them. The two-dimensional Navier-Stokes equations with one-step Arrhenius chemistry including the effects of viscosity, thermal conduction and molecular diffusion are used for the simulations. For comparison, simulations with Euler equations are also performed. The finite-volume operator splitting scheme used is based on the 2nd order Godunov-type, Weighted Average Flux (WAF) method with an approximate HLLC Riemann Solver. An Adaptive Mesh Refinement (AMR) technique is used to increase the resolution in areas of interest. The simulation results show that the interaction of the weak shock with the first cylindrical flame demonstrates very good agreement with the results in the literature and that a single weak shock-flame interaction was not enough to cause prompt DDT. However, a high degree of Richtmyer-Meshkov instabilities induced by repeated shock-flame interactions along with shock-boundary interactions generate turbulence that accelerates the flame brush, until eventually a hot spot ignition in the unreacted material develops into a multi-headed detonation wave. The simulation results also show that DDT is sensitive to the simulation method and that certain simulation parameters significantly affect the DDT phenomenon.