Large eddy simulation coupled with the third-order Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) differencing scheme was employed for investigating the ignition processes and flame structures of the reacting n-heptane spray over a wider range of diesel engine-relevant conditions. First, the effects of numerical schemes on the mixing and combustion processes are analyzed in detail. Comparisons of the mixture fraction profiles with experimental data from the Engine Combustion Network website show that the MUSCL gives a better prediction compared with Quasi-second-order upwind scheme. The mixing between fuel and air is much better using MUSCL scheme. As a result, ignition is initiated at fuel-leaner regions, but still richer than stoichiometric equivalence ratio. Second, the predicted ignition delay times and flame lift-off lengths are compared with experimental data under different initial conditions. The predicted results show good agreements with experimental results at different temperatures, oxygen concentrations, and densities. Finally, the effects of initial conditions on the spray flame structures are comprehensively analyzed using the temperature-equivalence ratio maps. The effects of initial parameters on the reacting spray structures and important radicals, such as OH and CO are investigated carefully. Results show that initial oxygen concentration has the greatest influence on the flame structures than ambient gas temperature and density.