高雷諾數奈維爾-史托克斯計算於靜止與加速物體流場之應用

Abstract

本論文主旨在於利用無網格數值方法以及沉浸邊界法來發展一套數值模式，並用來模擬研究複雜幾何以及移動邊界問題。通常這類型的模式必須具備著能夠有效地處理複雜幾何以及移動邊界的能力。首先在我們計算核心之中，我們提出一套無網格數值模式結合運算子拆解法來求解原始變數型態的奈維爾－史托克斯方程式，此無網格數值模式是結合尤拉－拉格朗日基本解法以及特解法所組成。接著將此模式應用在熱傳導以及移動物體問題上，藉此來驗證此模式的正確性和可靠性，同時在數值處理過程之中我們並不需要引用特殊的處理技巧來針對複雜幾何以及移動邊界。相對於無網格數值模式，最後本論文提出了另外一套數值模式用來準確的模擬移動邊界問題，此模式是利用有限差分法結合一套混合卡式沉浸邊界模式，而此模式的可靠性以及適用性可以經由一連串的數值實驗加以驗證，因此所提出的有限差分法結合混合卡式沉浸邊界模式在處理移動邊界問題上，可以視為一種有效率之數值方法。

In this dissertation, the major concern is developing the numerical models based on the meshless method and immersed boundary techniques to apply to the irregular geometry and moving obstacles. The developed model must be able to handle the complex geometry and moving boundary in an efficient procedure. In the core of the numerical simulations, first of all, a novel meshless procedure based on the Eulerian-Lagrangian method of fundamental solutions (ELMFS) and method of particular solutions (MPS) is presented for solving the primitive variable form of the Navier-Stokes equations by using operator splitting scheme. Then, the two-roll mill flow and closed cavity flow around a harmonic oscillating cylinder at moderate Reynolds number (Re=100~400 ) are solved to demonstrate the accuracy and the robustness of this meshless procedure. During the solution procedure, there are no any unusual techniques or restrictions need to be considered in order to deal with the irregular geometry and moving boundary. Finally, in contrast with the meshless procedure, the finite-difference method (FDM) with hybrid Cartesian/immersed- boundary (HCIB) technique is proposed as another solution to provide the accurate predictions for moving boundary problem. The flexibility and robustness of the proposed HCIB FDM are examined by 3D driven cavity flow with a stationary sphere and the flow fields due to motions and collisions of immersed spheres at high Reynolds number (Re>10,000 ), which demonstrate that the HCIB FDM can be considered as an efficient numerical method in solving the moving boundary problem.