Natural gas substitution for diesel can result in significant reductions in pollutant emissions. In addition, with a high ignition temperature and relatively low reactivity, natural gas can enable promising approaches to combustion engine design. In particular; the combination of low-reactivity natural gas and high-reactivity diesel may allow for optimal operation as a reactivity-controlled Compression ignition (RCCI) engine, which has potential for high efficiency and low emissions. In this computational study, a lean mixture of natural gas is ignited by direct injection of diesel fuel in part-load operating condition in a model of the heavy-duty CAT3401 diesel engine. A multi-dimensional simulation was performed using a finite volume computational code for fuel spray and combustion processes in the Reynolds-averaged Navier-Stokes (RANS) framework Adaptive mesh refinement (AMR) and multi-zone reaction modeling enables simulation in a reasonable time. The latter approach avoids expensive kinetic calculations in every computational cell, with considerable speedup. The model produces encouraging agreement between the simulation and experimental data. For reasonable accuracy and computation cost, a minimum cell size of 0.2 millimeters is suggested for the natural gas-diesel (NGD) dual-fuel engine. The results reveal that in part-load operating condition, much of the CH4, which is used as surrogate fuel for natural gas, cannot burn. The main goal of this research work is to assess the possibility to improve the performance of Caterpillar-3401 engine in NGD dual-fuel operation by in-cylinder modification strategies. The results reveal that among different strategies, double injection of diesel fuel with an early main injection can reduce the unburned hydrocarbon (UHC) emission significantly.