結合相場及水平集方程應用於多圖形顯示卡叢集之兩相流演算法

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研究生：	沈育任 Shen, Yu-Ren
論文名稱：	結合相場及水平集方程應用於多圖形顯示卡叢集之兩相流演算法 A phase-field coupled with level set method based on GPE solver for two-phase flow on GPU cluster
指導教授：	林昭安 Lin, Chao-An
口試委員:	牛仰堯 NIU, YANG-YAO 陳慶耀 Chen, Ching-Yao
學位類別：	碩士 Master
系所名稱：	工學院 - 動力機械工程學系 Department of Power Mechanical Engineering
論文出版年：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	52
中文關鍵詞：	兩相流、相場方程、水平集方程、弱可壓縮流、多圖形顯示卡叢集
外文關鍵詞：	Two-phase flow, Phase-filed, Level-set, Weakly compressible flow, GPU-cluster
相關次數：	點閱：2 下載：0
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在兩相流領域，介面捕捉及質量守恆一直都是重要的議題，為了解決此類問題有許多方法被提出。在本篇研究，筆者結合相場和水平集方程以兼顧上述數值要求。保守形式的相場方程擁有質量守恆的特性而水平集方程則是在計算介面的法向量及曲率上有較高準確度，因此結合這兩者優點可以達成一個更準確的兩相流演算法。
除此之外，為了加快圖形顯示卡(graphics processing unit)運算效率，本演算法採用顯式弱可壓縮流方程求解流場。

In two-phase ﬂow problems, interface capturing and mass conservation are always essential issues. A lot of methods were proposed to solve them. In this study, we present a phase-ﬁeld method coupled with the level set method. The conservative phase-ﬁeld method describing the interface with diﬀuse interface provides lots of desirable properties, while the level set method is good at estimating curvature and normal vector suitable for calculation of surface tension force. Combining the two methods can provide a more accurate two-phase ﬂow solver. Besides, for accelerating the eﬃciency of the simulation, a weakly compressible solver which is explicit and suitable for GPU is adopted.

Introduction 1
1 Motivation and objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 One fluid model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Surface tension force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Interface methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Methodology 11
1 Time-integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2 Conservative phase-field method . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1 Advection term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Diffusion and anti-diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Level set method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1 Advection term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Re-initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4 Navier-Stoke equation solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.1 Momentum equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 General pressure equation . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Result 22
1 Flow Field solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
iv
1.1 3D Lid-driven cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Validation of interface capture methods . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 Single vortex problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Two-phase flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 2D Static bubble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 2D Bubble Rising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 2D Dam Breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Conclusion 46
1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

                                

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