To develop an advanced numerical scheme, resolving all small-scale flow structures well meanwhile capable of capturing the discontinuities sharply and stably, is a long-term research topic of compressible fluid simulations. The inherent contradiction: low-dissipation is suggested for small-scale flow features whereas enough dissipation is required to suppress the numerical oscillations induced by discontinuities, makes it a stubborn problem. Several new concepts, e.g. artificial viscosity, total variation diminishing, essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) have been proposed to achieve the competing design targets. This project dedicates to developing new high-order numerical methods for predicting fluid flows over aircraft and contributes to optimizing the engineering quantities of interest, e.g., drag, lift, etc.