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姓名	陳重昱(Chung-Yu Chen)  查詢紙本館藏	畢業系所	數學系
論文名稱	(Numerical Computation of a Direct-Forcing Immersed Boundary Method for Simulating the Interaction of Fluid with Moving Solid Objects)
相關論文	★ 遲滯型細胞神經網路似駝峰行進波之研究 ★ 穩態不可壓縮那維爾-史托克問題的最小平方有限元素法之片狀線性數值解 ★ Global Exponential Stability of Modified RTD-based Two-Neuron Networks with Discrete Time Delays ★ 二維穩態不可壓縮磁流體問題的迭代最小平方有限元素法之數值計算 ★ 兩種迭代最小平方有限元素法求解不可壓縮那維爾-史托克方程組之研究 ★ 非線性耦合動力網路的同步現象分析 ★ 邊界層和內部層問題的穩定化有限元素法 ★ 數種不連續有限元素法求解對流佔優問題之數值研究 ★ 某個流固耦合問題的有限元素法數值模擬 ★ 高階投影法求解那維爾-史托克方程組 ★ 非靜態反應-對流-擴散方程的高階緊緻有限差分解法 ★ 二維非線性淺水波方程的Lax-Wendroff差分數值解 ★ On Two Immersed Boundary Methods for Simulating the Dynamics of Fluid-Structure Interaction Problems ★ 生成對抗網路在影像填補的應用 ★ 非穩態複雜流體的人造壓縮性直接施力沉浸邊界法數值模擬 ★ 模擬自由落體動力行為的接近不可壓縮直接施力沉浸邊界法
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摘要(中)	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。
摘要(英)	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.
關鍵字(中)	★ 不可壓縮納維爾-史托克方程 ★ 流固耦合 ★ 沉浸邊界法 ★ 投影法 ★ 直接施力法	關鍵字(英)	★ incompressible Navier-Stokes equations ★ fluid-solid interaction ★ immersed boundary method ★ projection method ★ direct-forcing method
論文目次	中文摘要 ……………………………………………………………………… i 英文摘要 ……………………………………………………………………… ii Contents ……………………………………………………………………… iii Abstract ……………………………………………………………………… 1 一 Introduction …………………………………………………… 2 二 Helmholtz-Hodge decomposition and Chorin’s projection method …………………………………………………………… 5 三 A two-stage direct-forcing immersed boundary projection method …………………………………………………………… 9 四 Spatial discretization in the projection computations … 12 五 Numerical experiments ………………………………………… 14 六 Concluding remarks ……………………………………………… 22 References …………………………………………………………………… 23
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指導教授	楊肅煜(Suh-Yuh Yang)	審核日期	2016-7-20
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