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研究生： 吳峙霆
Chih-Ting Wu
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
指導教授： 楊肅煜
Suh-Yuh Yang
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： 38
中文關鍵詞： 淺水波方程 、柯氏力 、Lax-Wendroff差分法 、Runge-Kutta法 、算子拆解法
外文關鍵詞： shallow water equations, Coriolis effect, Lax-Wendroff scheme, Runge-Kutta method, operator-splitting method
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    • 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。

    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.

    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

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