The ignition characteristics of lean primary reference fuel (PRF)/air/exhaust gas recirculation (EGR) mixture under reactivity-controlled compression ignition (RCCI) and direct duel fuel stratification (DDFS) conditions are investigated by 2-D direct numerical simulations (DNSs) with a 116-species reduced chemistry of the PRF oxidation. The 2-D DNSs of the DDFS combustion are performed by varying the injection timing of iso-octane (i-C8H18) with a pseudo-iso-octane (PC8H18) model together with a novel compression heating model to account for the compression heating and expansion cooling effects of the piston motion in an engine cylinder. The PC8H18 model is newly developed to mimic the timing, duration, and cooling effects of the direct injection of i-C-8 H-18 onto a premixed background charge of PRF/air/EGR mixture with composition inhomogeneities. It is found that the RCCI combustion exhibits a very high peak heat release rate (HRR) with a short combustion duration due to the predominance of the spontaneous ignition mode of combustion. However, the DDFS combustion has much lower peak HRR and longer combustion duration regardless of the fuel injection timing compared to those of the RCCI combustion, which is primarily attributed to the sequential injection of i-C8H18. It is also found that the ignition delay of the DDFS combustion features a non-monotonic behavior with increasing fuel-injection timing due to the different effect of fuel evaporation on the low-, intermediate-, and high-temperature chemistry of the PRF oxidation. The budget and Damkohler number analyses verify that although a mixed combustion mode of deflagration and spontaneous ignition exists during the early phase of the DDFS combustion, the spontaneous ignition becomes predominant during the main combustion, and hence, the spread-out of heat release rate in the DDFS combustion is mainly governed by the direct injection process of i-C8H18. Finally, a misfire is observed for the DDFS combustion when the direct injection of i-C8H18 occurs during the intermediate-temperature chemistry (ITC) regime between the first- and second-stage ignition. This is because the temperature drop induced by the direct injection of i-C8H18 impedes the main ITC reactions, and hence, the main combustion fails to occur. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.