應用異階有限元素法求解二維高雷諾數自由液面流場

本研究探討異階方程有限元素法求解自由液面流場的可行性。首先透過兩項常見的數值實驗驗證此計算流程的準確性，接著為了模擬二維自由液面流場，導入任意拉格朗日-尤拉演算法以及一粒子追蹤法，以處理自由液面中的移動邊界以及其相對應計算場域內部網格的移動。針對高雷諾數的流場，本研究引入上風無網格法，並結合有限元去做計算。本文最後將模式應用於液面的自由震盪與巨幅晃動問題，並討論其結果與模式可行性。

關鍵字

有限元素；異階元素方程式；任意拉格朗日-尤拉演算法；自由液面流；上游差分法

並列摘要

In this thesis, we study the finite element method of velocity-pressure formulation for free surface flows. In the beginning, we examine this formulation in mixed order interpolation finite element method by two classical numerical test problems. Afterwards, with a view to simulating the two-dimensional free surface flows, a particle tracking method and the arbitrary Lagrangian-Eulerian method will be applied to our model. Furthermore, an upwind scheme combined with a meshless method will also be taken into consideration to study the flow in high Reynolds number. Finally, we demonstrate and discuss the capability of this model by free oscillation and large amplitude sloshing problems.

並列關鍵字

Finite Element Method ； Mixed Order Formulation ； Arbitrary Lagrangian-Eulerian ； Upwind Scheme

參考文獻

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應用異階有限元素法求解二維高雷諾數自由液面流場

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