以最小平方有限元素法模擬三維插接血管流場

Numerical simulation of flow fields in a tube with branches by a least-squares finite element method

賴麒仰(Chi-Yang Lai)

指導教授 ： 鄧志浩

中原大學/工學院/土木工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500057

摘要

在兩分歧血管位於腹主動脈管的流場模擬過程中使用了最小平方有限元素法（LSFEM）此種數值分析的方法。在本文中考慮分歧血管位於動脈的同側或不同側兩種型式，在本研究中主要考慮兩分歧管之間的基本流場和可能發生交互影響的流場狀況。
當分歧血管位於同側時，我們發現到當分歧血管之間的距離越遠，兩根分歧管的交互影響越低，而其流場和剪力值分佈並不會跟單一分歧血管類似。另外在腹主動脈的背側和腹側靠近第一根分歧血管前端位置有低剪應力的產生。
當兩分歧血管位於不同側時，在主要管壁的末端發現迴流區域的產生。最有趣的例子為當兩根分歧管間的距離為零，在此例子中，流場和迴流區域皆為對稱形式。隨著兩分歧管的距離增大，迴流區域由背側端靠近第一根分歧管延伸到腹側端第二根分歧管的位置，而兩根分歧管之間的交互影響亦隨著距離增大而減少。
基於此種數值模擬方式，可以得到令人滿意和有效的數值模擬結果來模擬整個複雜的流場數值模型和實驗觀察。

關鍵字

最小平方有限元素法 ； 分歧管流 ； 剪應力 ； 迴流區域

並列摘要

A numerical calculation procedure based on the least-squares finite element method (LSFEM) is employed to simulate flow field in abdominal aorta with two branches. In this paper, the two branches are considered either on the same side or on the opposite side of the artery. The baseline flow fields and the possible flow interaction between the two branches is major concerned in this study.
When the two branches are on the same side we found that the flow field and shear stress distribution are not quite similar to that in a single-branched tube while the two branches are distant and the interaction between the two branches weakened as the distance inside the branches increased. Also, in both the ventral part proximal to the first branch and the dorsal part distal to the first branch there exists low shear stress area.
When the two branches are on the opposite side the reversed flow regions are found on the lateral walls of the main tube. While the distance between two branches is zero is the most interesting case. In this case, both the flow field and the reversed flow region are symmetrical. As the distance between two branches increasing the reversed flow region extends from the upper sides proximal to the first branch to the lower sides distal to the second branch. The interaction of flow field becomes weaker when the distance between two branches is longer.
Based on the numerical simulation, it can be concluded that this numerical model can simulate the whole complicate flow domain in good agreement with the available simulates results and the observed experiments.

Keywords: Least-squares finite element method, shear stress, reversed flow regions, two branches flow

並列關鍵字

Least-squares finite element method ； reversed flow regions ； shear stress ； two branches flow

參考文獻

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