本文的主要目的是實現文獻[11]中所提出的一種兩階段直接施力沉浸邊界投影方法模擬流體與移動固體交互作用的動力行為，其中每一沉浸固體都配有一個給定的速度。這個兩階段的方法結合了直接施力沉浸邊界投影方法和預測-修正策略，其中引入一個只分佈在固體上的離散虛擬力並將其附加到流體動量方程式來處理沉浸固體邊界上的無滑移邊界條件。具體來說，首先使用隱式尤拉公式去離散不可壓縮納維爾-史托克方程的時間變數並應用顯式一階的方法線性化其非線性對流項，然後採用預測-修正直接施力沉浸邊界投影法去求解時間離散後的方程式，在預測和修正階段中我們皆採用肖林時間一階的投影法。另外，對於投影法計算中的空間離散，我們採用交錯網格中央差分格式。我們執行兩個關於多個移動固體的數值實驗來說明此演算法的效率。數值結果顯示這個簡單的預測-修正沉浸邊界投影法對流固耦合問題可以求取合理的數值結果。;The aim of this thesis is to implement the two-stage direct-forcing immersed boundary projection method proposed by Horng et al. [11] for simulating the dynamics of fluid interacting with moving solid objects, where each immersed solid object is equipped with a prescribed velocity. This two-stage approach combines a directforcing immersed boundary projection method with a prediction-correction strategy, in which a discrete virtual force distributed on the solid object is introduced and appended to the fluid momentum equations to accommodate the no-slip boundary condition at the immersed solid boundary. Specifically, we first use the implicit Euler formula to discretize the temporal variable in the incompressible Navier-Stokes equations and apply the explicit first-order approximation to linearize the nonlinear convection term. We then employ a predicition-correction direct-forcing immersed boundary projection method to solve the time-discretized equations, where we adopt the first-order in time Chorin’s projection method in both prediction and correction stages. For spatial discretization in the projection computations, we employ the central difference scheme on the staggered grids. We give two numerical examples of multiple moving solid objects to illustrate the performance of the algorithm. From the numerical results, we find that this simple predicition-correction immersed boundary approach can achieve reasonable results for fluid-solid interaction problems.
