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研究生：	陳玟君 Wen-Jyun Chen
論文名稱：	Numerical Computation of Riemann Problem for a Degenerate Hyperbolic System of Conservation Laws
指導教授：	洪盟凱 Jhon M. Hong
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 數學系 Department of Mathematics
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	41
中文關鍵詞：	黎曼問題、愛因斯坦場方程、退化雙曲方程、數值計算
外文關鍵詞：	Degenerate hyperbolic system of Conservation laws, Riemann problem, Godunov's method, Euler's method
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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

在此篇論文中，我們主要探討 2x2 的退化雙曲方程對於黎曼問題的數值計算。此方程源自於愛因斯坦場方程的原型，我們將以一維非線性守恆態去建構簡易的退化雙曲方程，並用數值計算找出近似解。本研究中所使用的數值方法有Godunov's Method和Euler's Method，藉由不同的初始值來觀測我們的數值結果發散與否。最後歸納出來的結果及數據都可幫助我們在退化雙曲方程的問題上有更多的了解。

In this thesis, we study the numerical computation for the
Riemann problem of the 2x2 degenerate hyperbolic system
of conservation laws. The equations we consider is an
one-dimensional nonlinear balance laws, which can be considered as a warm-up system of shock wave model for the Einstein's field equations in spherical symmetric space-time. We will give a numerical method, which is called the Godunov method, to construct the approximate solutions for the Riemann problem. By giving several initial conditions for our numerical computation, we observer the consequences of existence or blow-up of solutions for Cauchy problem to the degenerate hyperbolic system.

中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
英文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Equations and the Numerical Methods . . . . . . . . . . . . . . . . . 3
2.1 Introduction to Degenerate Hyperbolic Equations . . . . . . . . . 3
2.2 The Riemann Problem for the equation . . . . . . . . . . . . . . . 3
2.3 Godunov's Method . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 The Euler's Method . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Numerical computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 The Algorithm of Numerical Method . . . . . . . . . . . . . . . . 11
3.3 Matlab Program for Godunov's Method . . . . . . . . . . . . . . 14
4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

                                

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