Abstract
With the invention of the aircraft, it has become much faster and larger than the original Wright Brothers aircraft. When the speed is high enough to cross the speed of sound, air conditions will be different than that in low speed due to the existence of shock wave. In this work, we introduce several numerical ways to analyze the performance of the airfoil when the speed is higher than the speed of sound. With these numerical methods, we analyzed the performance of diamond-shaped airfoil under different angles of attack and speed. With this data, engineers can choose a better airfoil to attain a lower drag coefficient as well as lift coefficient when designing a high-speed aircraft.

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