不可延展界面之斯托克斯方程的數值收斂研究

Numerical convergence study of Stokes equations with an inextensible interface

林文禹(Wen-Yeu Lin)

指導教授 ： 賴明治

國立交通大學/理學院/數學建模與科學計算研究所/碩士(2018年)

摘要

在本篇論文中，我們發展了一個在二維，解含有不可延展界面之斯托克斯方程的數值方法，並且對於鬼點(ghost point)使用二次外插(而非傳統的線性外插)的原因，給出了解釋。構造這個問題的解析解方法，也一併在本篇論文給出，使得我們可以討論所有變數的數值誤差。最後，我們展示一些對於利用這些方法構造出來的例子的數值結果，以及在最後的小節，給出一些結論。

關鍵字

沉浸邊界法 ； 不可延展界面 ； 斯托克斯方程

並列摘要

In this paper, we develop a numerical scheme for solving Stokes equations with an inextensible interface in 2D and explain the reason that we use quadratic extrapolation instead of the standard linear extrapolation to extrapolate the ghost points. Methods that construct the analytic solutions of the problem are shown in this paper hence we can discuss the errors of all variables. Finally, we display the numerical results of some examples that constructed by those methods and some conclusion will be given in the last section.

並列關鍵字

immersed boundary method ； inextensible interface ； Stokes equations

參考文獻

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