The present work examines numerically the aerodynamic breakup of Diesel and heavy fuel oil (HFO) droplets in ambient pressures ranging from atmospheric up to those encountered in Diesel engines. The numerical model solves the Navier-Stokes equations coupled with the Volume of Fluid (VOF) methodology along with an adaptive local grid refinement technique to enhance the resolution near the high deformable interface. Simulations are performed both in 2D axisymmetric and 3D computational domains. The capabilities of the model are evaluated by comparing its results against published experimental data for Diesel fuel droplets at small Ohnesorge numbers (Oh<0.04), Weber (We) numbers ranging from 14 up to 264, and liquid to air density ratios (ε) from 79 up to 695. These conditions correspond to the bag, multimode and sheet-thinning breakup regimes. Following model validation for Diesel droplets, the breakup mechanism of HFO droplets is investigated for the same range of We numbers, two relatively large Oh numbers (0.96 and 1.53) and two density ratios (30 and 72); these conditions are representative for Diesel engines operating with HFO. The simulations reveal the effect of Oh number and density ratio on the breakup mode, drop deformation, liquid surface area and drag coefficient. Finally, a correlation is proposed for the prediction of the breakup initiation time as function of the non-dimensional numbers We, Re, ε and Oh