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研究生：	胡澔剛 Hu, Benjamin
論文名稱：	號誌化環狀道路下的有效車流分析與計算 Computing effective flow rates for a signalized ring road
指導教授：	劉育佑 Liu, Yu-Yu
學位類別：	碩士 Master
系所名稱：	理學院 - 數學系應用數學碩博士班 Department of Mathematics
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	32
中文關鍵詞：	不連續介面的 Godunov 數值方法、LWR 交通流模型、Greenshield 車流模型、有效車流
外文關鍵詞：	Discontinuous Godunov scheme, LWR model, Greenshield, Effective flow rates
相關次數：	點閱：92 下載：20
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查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本論文提供一個數值方法來求解一個在介面處有斷點並且符合守恆律的不連續流體，並且應用於交通流量模型來處理受干擾的車流，特別是受號誌影響的情況下。此數值方法是在Godunov 數值方法的架構下，對介面處做些特別的處理。
接著根據此數值方法做些交通相關的數值模擬並跟解析解做比較。最後將此應用於以 Greenshield 模型模擬車流並設有號誌的環狀道路中，然後分析此結果。

In this research, a novel numerical scheme is proposed to solve the problem of conservation laws with discontinuous interface and the proposed scheme is then applied to solve the Lighthill, Whitham and Richards (LWR) model under interrupted flows, especially flows influenced by the signals. The proposed scheme is constructed based on the Godunov’s scheme with special treatment at interfaces.
The proposed scheme is then illustrated and evaluated through different numerical experiments and the numerical results are compared with those obtained from analytical models.
Then the proposed scheme is applied to solve the problem of the LWR model with signals in the ring road under the assumption of the Greenshield function.

摘要i
Abstract ii
Acknowledgements iii
Table of Contents iv
List of Figures v
Chapter 1. Introduction 1
Chapter 2. Numerical approximation for conservation laws 3
2.1 Conservation Laws and LWR model . . . . . . . . . . . . . . . . . . . . . 3
2.2 Numerical Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Riemann problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Godunov scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5 CFL condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3. Traffic Scenario 9
3.1 Greenshield’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Godunov scheme when flow is discontinuous . . . . . . . . . . . . . . . . 10
3.3 Bottleneck problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Chapter 4. Analysis for a signalized ring road I : Numerical method 16
4.1 The LWR model on traffic ring road . . . . . . . . . . . . . . . . . . . . . 16
4.2 Numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Chapter 5. Analysis for a signalized ring road II : Flow rates 24
5.1 Cumulative flow and its flow rate . . . . . . . . . . . . . . . . . . . . . . . 24
5.2 Macroscopic fundamental diagram of Triangle fundamental diagram model 26
5.3 MFD of the Greenshield model . . . . . . . . . . . . . . . . . . . . . . . . 28
Chapter 6. Conclusion 31
References 32
                                    

[1] Adimurthi, Jérôme Jaffré, and G. D. Veerappa Gowda. Godunovtype methods for conservation laws with a flux function discontinuous in space. SIAM Journal on Numerical Analysis, 42(1):179–208, 2005.
[2] WenLong Jin and Yifeng Yu. Performance analysis and signal design for a stationary signalized ring road. https://arxiv.org/abs/1510.01216, 2015.
[3] Randall J. LeVeque. Godunov’s Method, pages 136–145. Birkhäuser Basel, Basel, 1990.
[4] S. Mishra. Chapter 18 numerical methods for conservation laws with discontinuous coefficients. In Rémi Abgrall and ChiWang Shu, editors, Handbook of Numerical Methods for Hyperbolic Problems, volume 18 of Handbook of Numerical Analysis, pages 479 – 506. Elsevier, 2017.
[5] G.F. Newell. A simplified theory of kinematic waves in highway traffic, part i: General theory. Transportation Research Part B: Methodological, 27(4):281 – 287, 1993.

校內：2021-07-26公開
校外：2021-07-26公開

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