在本論文中，利用數值方法模擬振翅翼之流場，分析其空氣動力。數值方法是以有限體積法來求解尤拉方程式（Euler equation）。其中空間採用高階向風有限體積化，時間積分是採用對角化交叉方向隱式法（DDADI）數值方法來處理。為了加速數值上的收斂性，引入隱式殘值平滑法。
　　
　　對於振翅翼的空氣動力分析，吾人選定由二維翼剖面組合NACA0018之翼剖面為機體，NACA2412之翼剖面為機翼組合而成的三維格點，針對不同的振翅頻率、不同俯仰角、不同的流場攻角、不同的翅膀形狀來進行分析與研究。結果得知在振翅頻率K為0.2下擁有較好的效率，俯仰角可以使得飛行更省力，而梯形翼的效率比直角翼來得好。

　　A numerical method is developed to study the flapping wing flowfields. The method uses finite-volume method to solve the Euler equation. A diagonal dominant alternating direction implicit scheme (DDADI) coupling with an implicit residual smoothing is used for the time integration to achieve fast convergence of the proposed scheme. The upwind scheme is a MUSCL-type scheme.

　　For aerodynamic performance on the flapping wings. Body of NACA0018 airfoil and wing of NACA2412 airfoil are chosen for studing. Quantitative understanding the effects of the flapping frequency, mean angle of attack, pitching angle and wing shape are calculated. There is a better propulsion efficiency at reduce frequency of. Reversed trapezoidal wing has a better propulsion efficiency than Rectangular wing and trapezoidal wing.

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