Numerical grid and time-step dependencies of discrete droplet Lagrangian spray models are identified. The two main sources of grid dependency are due to errors in predicting the droplet-gas relative velocity and errors in describing droplet-droplet collision and coalescence processes. For reducing grid dependency due to the relative velocity effects, a gas-jet theory is proposed and applied to model diesel sprays. For the time-step dependency, it is identified that the collision submodel results in drop size variation in the standard spray model. A proposed spray model based on the gas-jet theory is found to improve the time-step independency also along with the mesh independency. The use of both Eulerian (collision mesh) and Lagrangian (radius of influence) collision models along with the gas-jet theory is found to provide mesh-independent results.