廣義黎曼解決方案等溫可壓縮歐拉 - 泊松方程流球對稱空間時代

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馬葵娜(Reyna Marsya Quita) 查詢紙本館藏

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數學系

論文名稱

廣義黎曼解決方案等溫可壓縮歐拉 - 泊松方程流球對稱空間時代
(Generalized Riemann Solutions to Compressible Euler-Poisson Equations of Isothermal Flows in Spherically Symmetric Space-times)

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摘要(中)

在本文中，我們考慮球對稱空間時間可壓縮歐拉方程泊松。方程，代表品質和重力吸引潛在的物理量動量守恆，可以寫成一個混合型的3x3部分迪系統的差動或平衡法與全球源2X2雙曲系統。我們展示的方程為品質守恆，歐拉 - 泊松下方程可以轉化為平衡定律與本地源純3x3的雙曲系統。歐拉 - 泊松方程黎曼問題，這是在初始邊值問題廣義Glimm方案的構建塊的通用解決方案，提供不嚴的類型相關聯的同質守恆定律弱解和擾動項解決了疊加通過與些線性雙曲系統與這種鬆懈的解決方案。最後，我們提供LAX-Wendroff無限迪方法和辛普森的數值積分為某些初始邊值問題全球資源。提供了幾種類型的初始和邊界資料的數值類比。

摘要(英)

In this thesis, we consider the compressible
Euler-Poisson equations in spherically symmetric space-times. The
equations, which represent the conservation of mass and momentum
of physical quantity with attracting gravity potential, can be
written as a mixed-type $3 imes 3$ partial differential systems
or an $2 imes 2$ hyperbolic systems of balance laws with $global$
source. We show under the equation for the conservation of mass,
Euler-Poisson equations can be transformed into a pure $3 imes 3$
hyperbolic system of balance laws with $local$ source. The
generalized solutions to the Riemann problem of Euler-Poisson
equations, which is the building block of generalized Glimm scheme
for the initial-boundary value problem, are provided as the
superposition of Lax′s type weak solutions of associated
homogeneous conservation laws and the perturbation terms solved by
some linearized hyperbolic system with coefficients related to
such Lax′s solution. Finally, we provide Lax-Wendroff finite
difference method and Simpson′s numerical integration to the
global sources for some initial-boundary value problems. Numerical
simulations are provided for several types of initial and boundary
data.

關鍵字(中)

★ 可壓縮歐拉 - 泊松方程
★ 初始邊值問題
★ 弱解
★ 廣義黎曼問題
★ 寬鬆的方法
★ 線性化

關鍵字(英)

★ Compressible Euler-Poisson equations
★ initial-boundary value problem
★ weak solutions
★ generalized Riemann problem
★ Lax method
★ linearization

論文目次

1 Introduction 2
2 Re-formulation of Euler-Poisson Equations 8
3 Construction of Approximate Solution of (2.8) and (2.9) 11
4 Numerical Method and Simulations for Euler-Poisson Equations 20
4.1 The Finite Difference Method 20
4.2 The Lax-Wendroff Method 21
4.3 Numerical Simulations 22

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指導教授

洪盟凱(John M. Hong)

審核日期

2016-8-22

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