Lean combustion turbines provide excellent opportunities for environmentally friendly propulsion and electricity generation, but are severely limited by the danger of autoignition of the fuel-air mixture before its proper location. Further development of next-generation devices hinges upon better understanding of autoignition in flows that are characterized by considerable fluctuations of velocity, composition, and temperature. The aim of this project is to study the fundamental aspects of autoignition in a fuel-air mixing pattern directly applicable to mixing ducts in gas turbines. The Nek5000-based combustion code will be used to perform very large-scale direct numerical simulations of autoignition of a diluted hydrogen jet in a cross-flow of hot turbulent air in a laboratory-scale configuration. Detailed description of chemistry and molecular transport will be used to investigate the flow and scalar fields under cold and reactive conditions. It will also be used to construct databases that will be explored for years by engineers and scientists working in engine development for the construction and validation of advanced combustion models for engineering-type computational fluid dynamics codes.