This paper summarizes a 10-year theoretical and numerical effort to understand the deflagration-to-detonation transition (DDT). To simulate DDT from first principles, it is necessary to resolve the relevant scales ranging from the size of the system to the flame thickness, a range that can cover up to 12 orders of magnitude in real systems. This computational challenge resulted in the development of numerical algorithms for solving coupled partial and ordinary differential equations and a new method for adaptive mesh refinement to deal with multiscale phenomena. Insight into how, when, and where DDT occurs was obtained by analyzing a series of multidimen¬sional numerical simulations of laboratory experiments designed to create a turbulent flame through a series of shock-flame interactions. The simulations showed that these interactions are important for creating the conditions in which DDT can occur. Flames enhance the strength of shocks passing through a turbulent flame brush and gen¬erate new shocks. In turn, shock interactions with flames create and drive the turbulence in flames. The turbulent flame itself does not undergo a transition, but it creates conditions in nearby unreacted material that lead to ignition centers, or "hot spots," which can then produce a detonation through the Zeldovich gradient mechanism involving gradients of reactivity. Obstacles and boundary layers, through their interactions with shocks and flames, help to create environments in which hot spots can develop. Other scenarios producing reactivity gradients that can lead to detonations include flame-flame interactions, turbulent mixing of hot products with reactant gases, and direct shock ignition. Major unresolved questions concern the properties of nonequilibrium, shock-driven turbulence, stochastic properties of ignition events, and the possibility of unconfined DDT.
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