本文提出於非交錯性直角坐標網格系統之隱式虛擬邊界法來計算移動邊界問題，並搭配補綴網格(patch gird)的使用，可以大幅提高運算效率，且可以大幅的減低記憶體的佔用。本文透過於沉浸邊界附近之流體格點施加一個外力，將沉浸邊界之影響加入流場的計算中，而此外力可直接由流場和物體邊界之條件求得，使計算流程更為簡單。本文使用隱式法來處理暫態項，可以允許計算較大的時間步階。之後，本文應用隱式虛擬邊界法針對三個案例進行計算。第一個案例是移動邊界問題，計算蜻蜓進行拍翅運動之流場，並計算蜻蜓拍翅所產生之力量；第二個案例是混合熱對流問題，此案例會加入溫度場之計算，計算密閉方形容器內置入一轉動平板之流場與溫度場，並透過紐塞數來討論熱傳之效果；第三個案例是流固耦合問題，本文會提出一個簡單的方法來計算懸臂樑的大振幅振動，先透過自由振動來驗證新方法之正確性，而後，將流場之效應加入懸臂樑振動之計算，觀察黏滯阻尼對振動之影響，此案例中，流場與振動會互相影響，而隱式虛擬邊界法與振動計算之方法可以簡單的將彼此之影響加入計算當中。

In this paper, a simple numerical method is proposed solving fluid flow around irregularly moving bodies. The computational domain of fluid is performed on non-staggered Cartesian grid system. Using patch gird can significantly enhance the efficiency of computation and reduce the usage of storage. We apply the implicit scheme for unsteady term such that large time step is allowed. The influence of immersed boundary on fluid field through imposes an external force at each fluid grid adjacent to immersed boundary. The implicit virtual boundary method is using to solve the following three cases. First, a moving boundary problem is about the flow induced by the flapping wings of a tethered dragonfly. Second, a mixed convection problem is about a rotating flat plate in a square enclosure. The natural convection is due to the different temperature of two vertical walls. The forced convection is caused by the rotating plate. And discuss the heat transfer efficiency by the Nusselt number. Third, a fluid-structure interaction problem is about the viscous damping vibration of cantilever beam. A numerical method is proposed calculating the large-amplitude vibration. The case of free vibration is used for verify the correctness of the new method. Then, calculate the vibration with viscous damping effect from fluid filed. In this work, the fluid-structure interaction (FSI) problem can easily solve by coupled with the proposed new method and the implicit virtual boundary method.

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