A Parallel Multilevel Semi-implicit Scheme of Fluid Modeling for Numerical Low-Temperature Plasma Simulation

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邱垂青(Chuei-Ching Chiou) 查詢紙本館藏

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論文名稱

(A Parallel Multilevel Semi-implicit Scheme of Fluid Modeling for Numerical Low-Temperature Plasma Simulation)

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摘要(中)

由於電漿在許多工業及生醫領域廣泛地被應用並且在其中扮演重要角色，因此對電漿本質及特性的了解在應用層面上顯得越來越重要。因為實驗所必須付出的高成本，以及某些物理量測上的困難，數值模擬在此時發揮其價值，用作預測及驗證。在恰當的物理環境條件下，例如：背景氣體溫度約為 300K，非過於稀薄氣體壓力( >50 mTorr)，流體模型是一項合適於研究低解離電漿的有力工具。又歸功於近代電腦設備進步以及平行計算的發展，電漿數值模擬在耗費在計算上的時間得以減低。
然而，為了更貼近實際應用面及真實的問題，取得有具體參考價值及意義的模擬，多維度(2維或3維)的模擬以及複雜化學反應的考量往往是無可避免的，因此，線性系統求解的效率及程式在平行計算上的表現仍然是需要探討研究的議題。
在本篇論文當中，我們列出半離散格式的推導，以及一些應用KSP (Krylov-subspace)迭代法求解而得的數值結果，其中包括應用或未應用多重網格法當作先處理的兩類情況。我們將對於所呈現的結果做一些比較及討論，評估多重網格法應用在低溫電漿模擬之效益。最後，針對多重網格法的研究以及平行程式的開發的面向，提出可在未來延續的研究方向及目標。

摘要(英)

Since plasma is widely applied and plays an important role in many industrial and biomedical fields, the fundamental understandings of plasma is becoming more and more essential for practical applications. Due to the high costs of physical experiments and high difficulties on measurements, numerical simulations is needed for predictions or validations. For studying the low-discharged plasma which is under low-temperature (~300K) and pressure is not too low (> 50 mTorr), fluid model is one suitable tool for simulations. For the advance in computer hardware and parallel computing, the computational runtime of a plasma simulation can be reduced.
However, the computational efficiency of linear system solvers and performance on parallel computing are still issues, since the multi-dimensional (2- or 3-dimensional) simulations and considerations of complex chemistry are often required for a realistic plasma simulation to cope with practical problems and applications.
In this thesis, we give the derivations of semi-implicit scheme and present some results of a simulation case while KSP (Krylov-subspace) iterative methods are applied with or without multigrid method is applied as a preconditioner. As conclusions of this thesis, we make some comparisons and comments for the efficiency with application of multigrid methods to plasma fluid modeling simulations. Finally, we state the future works for some aspects such as researches on multigrid mehtods and developments of parallel fluid modeling code.

關鍵字(中)

★ 低溫電漿
★ 多重網格法
★ 電漿模擬
★ 半隱式格式

關鍵字(英)

★ plasma simulation
★ semi-implicit scheme
★ multigrid method
★ low-temperature plasma

論文目次

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Specific Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Plasma Fluid Modeling Equations . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Numerical Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Semi-Implicit Treatment of Poisson Equation . . . . . . . . . . . . . . . . . 8
3.3 Scharfetter-Gummel Scheme for Mass Fluxes . . . . . . . . . . . . . . . . . 9
3.4 Implicit Treatment of the Electron Energy Source Term . . . . . . . . . . . 12
3.5 Remarks for Solution Algorithm and Discretization Equation . . . . . . . . 15
3.5.1 Components of Linear System Matrix . . . . . . . . . . . . . . . . . 15
3.5.2 Solution Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Multigrid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Two-Grid Correction Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Prolongation and Restriction . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 Coarse Grid Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.5 V-Cycle Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.1 Problem Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2 Numerical Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . 25
6 Conclusions and Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1 Contours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Some Spectrums of Linear System Matrices . . . . . . . . . . . . . . . . . 36

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指導教授

黃楓南(Feng-Nan Hwang)

審核日期

2012-7-24

推文