博碩士論文 100221027 詳細資訊




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姓名 吳峙霆(Chih-Ting Wu)  查詢紙本館藏   畢業系所 數學系
論文名稱 二維非線性淺水波方程的Lax-Wendroff差分數值解
(Lax-Wendroff Difference Solutions of the 2-D Nonlinear Shallow Water equations)
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摘要(中) 在本文中,我們將考察具柯氏力項的二維非線性淺水波方程有限差分數值解。利用二階Runge-Kutta法與算子拆解法對時間變數進行離散化,我們推導出兩種Lax-Wendroff類型的有限差分數值解法,這兩種方法在時間與空間變數的離散上均能維持二階的精確度。我們將選取反射型的邊界條件及數種不同的初始條件進行一系列的數值模擬實驗。經過大量的數值模擬後,我們發現以Runge-Kutta法為基礎的Lax-Wendroff有限差分數值解似乎具較高的穩定性。
摘要(英) In this thesis, we will investigate the finite difference schemes for solving the 2-D nonlinear shallow water equations with the Coriolis effect. Based on the second-order Runge-Kutta method and the operator-splitting method for time discretization, we derive two Lax-Wendroff-type finite difference schemes. Both proposed finite difference schemes possess the second-order accuracy in temporal and spatial variables. We will apply the reflective boundary condition with various initial conditions to perform a series of numerical simulations. From the numerical results, we find that the proposed scheme based on the Runge-Kutta method seems having a better stability.
關鍵字(中) ★ 淺水波方程
★ 柯氏力
★ Lax-Wendroff差分法
★ Runge-Kutta法
★ 算子拆解法
關鍵字(英) ★ shallow water equations
★ Coriolis effect
★ Lax-Wendroff scheme
★ Runge-Kutta method
★ operator-splitting method
論文目次 中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Lax-Wendroff-type finite difference schemes . . . . . . . . . . . . . . . . . . . . . . 7
4 Numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
參考文獻 [1] J. Burkardt, Numerical solution of the shallow water equations, available at
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[2] C. Lu and J. Qiu, Simulations of shallow water equations with ¯nite di®erence Lax-
Wendro® weighted essentially non-oscillatory schemes, Journal of Scienti¯c Comput-
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[3] E. T. Flouri, N. Kalligeris, G. Alexandrakis, N. A. Kampanis, and C. E. Synolakis,
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[8] R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Univer-
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[9] C. Moler, Experiments with MATLAB, MathWorks, Inc., 2011, available at
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[10] G. Ri°et, SHEL, a SHallow-water numerical modEL: Technical Guide v0.2, Maretec
IST-UTL, 2010, available at https://code.google.com/p/shel/
[11] M. C. Shiue, J. Laminie, R. Temam, and J. Tribbia, Boundary value problems for
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[12] J. W. Thomas, Numerical Partial Di®erential Equations: Finite Di®erence Methods,
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指導教授 楊肅煜(Suh-Yuh Yang) 審核日期 2013-7-29
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