Three time integration schemes and four finite volume interpolation schemes for the convection term in momentum equation were tested under turbulent planar gas jet and Sandia non-reacting vaporizing Spray-H cases. The three time integration schemes are the first-order Euler implicit scheme, the second-order backward scheme, and the second-order Crank-Nicolson scheme. The four spatial interpolation schemes are cubic central, linear central, upwind, and vanLeer schemes. Velocity magnitude contour, centerline and radial mean velocity and Reynolds stress profiles for the planar turbulent gas jet case, and fuel vapor contour and liquid and vapor penetrations for the Diesel spray case predicted by the different numerical schemes were compared. The sensitivity of the numerical schemes to mesh resolution was also investigated. The non-viscosity based dynamic structure subgrid model was used. The numerical tool used in this study was OpenFOAM. Results showed that the first-order Euler implicit schemes predict wider range of length scales as seen in velocity and fuel vapor contour plots, while the second-order time integration schemes predict more small scale structures. The non-monotonic central schemes show less grid sensitivity than the monotonic schemes. Overall the cubic central scheme with the Euler implicit scheme gives the best performance. The first-order upwind scheme gave poor results, so it should be avoided to use in simulating high-pressure fuel injection process.