Direct numerical simulation (DNS) and large eddy simulation (LES) approaches that employ detailed chemistry and transport properties are used to study the mechanisms responsible for the onset of auto-ignition, and the structures and dynamics of the reaction front propagation in reactivity controlled compression ignition (RCCI) combustion mode. This research is motivated by the public concerns on global warming due to emissions of the greenhouse gas CO2, as well as emission of pollutants (soot, NOx, CO, and unburned hydrocarbons) from fossil fuel combustion in internal combustion engines. The goals of the DNS work is to achieve improved understanding of the physical and chemical processes in the RCCI processes. The goals of the LES work is to validate various combustion model (well-stirred reactor, transport PDF and flamelet generated manifold) under RCCI dual fuel condition relevant to ECN SprayA condition. And then “single-fuel” RCCI concept will be studied based on low-temperature reform and catalytic reform. The following fundamental issues are to be investigated: a) the onset of auto-ignition and lean premixed flame propagation process under different reform degree; b) the structures and dynamics of the reaction fronts under different injection time; c) the effect of turbulence, the stratifications in temperature and charge, and the loads (mean temperature and pressure in the cylinder) on the auto-ignition and reaction front propagation.