整合沉浸邊界法與寬頻元素法之流固耦合數值模擬工具

Development of a Spectral Element-Immersed Boundary Method for Fluid-Structure Interaction Problems

陳立杰(Li-Chieh Chen)

指導教授 ： 黃美嬌

國立臺灣大學/工學院/機械工程學研究所/博士(2017年)

https://doi.org/10.6342/NTU201700046

摘要

在本論文中整合了沉浸邊界法與寬頻元素法，用以模擬二維之流固耦合問題。沉浸邊界法用以快速捕捉移動固體與流體之間的交互作用,固定且複雜的邊界則利用寬頻元素法的幾何彈性捕捉。在本方法中使用了非均勻密度的虛擬區域法(fictitious domain method)以及直接力量-虛擬區域法(direct forcing fictitious domain)兩種不同類型的沉浸邊界法以模擬剛體與不可壓縮流體間的交互作用。前者在固體區域內填入與固體密度相同的流體，將整個計算區域視為一非均勻密度的流場，再以固體區域內的動量估算剛體運動，最後以懲罰模型強制固體範圍內流體以剛體方式運動。後者同樣將流體延伸進固體區域，但填入與外部流體相同之流體，並在流體範圍內加入一假想力以耦合流固行為。為了解決流固邊界上性質的不連續，本論文提出了一分晶胞法將不連續性平滑化。此分晶胞法也同時幫助我們執行固體範圍內各性質的積分。經由模擬各類經典的流場實驗以及比對文獻或解析解的結果，本方法的準確性得到了驗證。最後根據研究剛體的經驗，我們將本方法延伸至處理可變形固體上，並在論文中簡單介紹初步結果。

關鍵字

沉浸邊界法 ； 寬頻元素法 ； 流固耦合 ； 分晶胞法 ； 虛擬區域法

並列摘要

To simulate two-dimensional two-way coupling problems between a rigid body and a fluid, we combine the immersed-boundary type method with the spectral element method; the former is employed for efficiently capturing the two-way FSI (fluid-structure interaction) and the geometric flexibility of the latter is utilized for any possibly co-existing stationary and complicated solid or flow boundary. Two immersed-boundary type methods are chosen in this work. The first one is the FD (fictitious domain) method. In this method, the solid region is filled with a fictitious fluid having a density as the same as the solid, and the entire fluid-solid domain is treated as an incompressible fluid with non-uniform density. The momentum inside the solid region is used to estimate the rigid-body motion and the no-slip boundary condition at the rigid body surface is enforced by the penalization method. The second one is the DFFD (direct forcing fictitious domain) method. The fluid in the fluid region is extended into the solid region and pseudo body force is imposed within the solid domain to enforce the rigid body motion in this method. In particular, a so-called sub-cell scheme is proposed to smooth the discontinuity at the fluid-solid interface and to execute integrations involving Eulerian variables over the moving-solid domain. The accuracy of the proposed method is verified through an observed agreement of the simulation results of some typical flows with analytical solutions or existing literature. Meanwhile, besides the rigid body, we also attempt to deal the deformable material. Some preliminary results are shown in the thesis.

並列關鍵字

immersed boundary method ； spectral element method ； fluid-structure interaction ； sub-cell ； fictitious domain

參考文獻

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