Transient flame propagation in fuel droplet arrays is investigated using three-dimensional numerical analyses with two different computational approaches. Flame propagation characteristics of fuel droplet arrays are first examined using a relatively new, but computationally expensive, method for two-phase reacting flow numerical simulations called the Level-Set approach, capable of tracking the gas-liquid interface movement. Next, the validity and effectiveness of the computationally cheaper Particle-Source-In-Cell (PSI-Cell) approach are verified for the prediction of flame propagation characteristics of fuel droplet arrays. The fuel constituting the droplets is n-decane (n-C10H22). Reaction mechanism for n-decane combustion is described using a two-step overall reaction model, based on a widely used reduced two-step chemical scheme originally developed for kerosene flames. The reaction model is validated against a detailed reaction mechanism for n-decane combustion. Results of the investigations using Level-Set approach reproduce the three different modes of flame propagation in fuel droplet arrays as observed in experiment, and show that the flame propagation speed is accurately predicted for each mode. Radiative heat transfer has an appreciable influence on the flame propagation speed. Furthermore, the application of a Gaussian function filter to the calculation of source terms accounting for the liquid phase-gas phase interactions, in the computations using PSI-Cell approach is adopted. Using this technique, the three flame propagation modes are reproduced for the fuel droplet arrays, and their corresponding flame propagation speeds are also accurately predicted.