Computational fluid dynamics can be time consuming for predicting indoor airflows and pollutant transport in large-scale problems or emergency management. Fast fluid dynamics (FFD) is able to accomplish efficient and accurate simulation of indoor/outdoor airflow. FFD solves the advection term of the Navier-Stokes equations either by a semi-Lagrangian (SL) scheme or an implicit upwind (IU) scheme. The SL scheme can be highly efficient, but its first-order version is not conservative and introduces significant numerical diffusion. To improve its accuracy, a high-order temporal and interpolation scheme that not only reduces dissipation and dispersion errors but also guarantees the convergence speed should be applied. Otherwise, an IU scheme instead could be used to solve the advection term. The IU scheme is conservative and introduces minor numerical diffusion, but it may increase the computation time. Therefore, this study investigated the performance of FFD with SL scheme using high-order temporal and interpolation schemes and that with IU scheme. The comparisons used experimental data of two indoor airflows and one outdoor airflow. The results showed that FFD with IU scheme was overall more accurate than FFD with SL scheme. In simulating indoor airflow, both methods were robust and the predictions were independent of time step sizes if the Courant number was less than or equal to one. In simulating the outdoor airflow, the FFD with SL scheme performed better than the FFD with IU scheme for large time step sizes. The FFD with IU scheme consumed 44%-61% computing time of the FFD with SL scheme.