無網格內插修正有限體積法求解熱流問題之數值模擬

Numerical Simulations of Thermal and Fluid Problems by Meshless Approximated Finite Volume Method

周情凱(Ching-Kai Chou)

指導教授 ： 楊德良

國立臺灣大學/工學院/土木工程學研究所/博士(2019年)

https://doi.org/10.6342/NTU202000567

摘要

本論文致力於開發全新無網格近似有限體積數值方法求解熱流場及其衍伸之工程應用問題。期間輔以開發混合非對接網格、沈浸物體方法及無網格高精度近似等相關技術，以突破傳統網格類數值方法於高度複雜幾何問題中網格生成及幾何退化等困境。文中首先針對熱流問題之物理背景、控制方程式、邊界及起始條件進行介紹，並針對其衍伸化簡方程及其應用問題進行說明。其後闡述無網格近似修正有限體積方法之相關資料定義及離散方法且進行數值精確度與穩定性之基礎驗證，並以非線性流場迭代演算方法為例說明其易適用於各式工程應用與數值模擬。隨後演示相關技術應用於二維與三維之勢流場、不可壓縮內外流場、溫度密度驅動場、流固互制及二相非牛頓流體場並進行案例比對與探討。於此經由本論文所提出之無網格近似有限體積法能有效結合無網格類方法與傳統網格類方法之優勢並改善其缺失，並於未來擁有極大潛力解決各式工程模擬應用問題。

關鍵字

無網格內插修正有限體積法 ； 納維爾-斯托克斯方程 ； 無網格方法 ； 有限體積方法

並列摘要

The present research aims to develop a novel Meshless Approximated Finite Volume Method (MAFVM) solving thermal & fluid problems and which corresponding engineering applications. There are developed some techniques correspondingly such as non-matching (hybrid) mesh, immersed objects, and high-order meshless approximated techniques. Those developing techniques can overcome the difficulty in mesh generation with complex geometries and preserve the accuracy and generality simultaneously when the defects happened in the degenerate mesh cases. At the beginning of this dissertation, the knowledge of the physical background and governing equations will be introduced, then boundary and initial conditions will also be presented separately in the general thermal and fluid problems. Moreover, those corresponding reduced governing equations are also defined and described with different applications individually. We elaborate on the data format and numerical methodology for our proposed MAFVM scheme at the beginning then its discretized formulation for general conservation equations will also be derived in the following paragraph. Besides, the accuracy and the robustness will be verified and demonstrate with two- and three- dimensional benchmark cases including potential flow, incompressible flow in the internal and external field. Especially, the time integration algorithm plays an important role in the highly nonlinear flow problem that there are several schemes also be introduced in detail. Our proposed MAFVM is prone to employ within various engineering problems and applications, further, industry. There are some advanced problems such as two-phase non-Newtonian fluid, fluid-structure interaction and injection molding problems also be illustrated in the rest of the dissertation. Therefore, we can approve our proposed MAFVM scheme integrate advantages from mesh-free type methods and some disadvantages improved from the traditional mesh-type methods. Importantly, the method has great potential to solve various engineering and applicated problems in the future.

並列關鍵字

Meshless Approximated Finite Volume Method(MAFVM) ； Navier-Stokes equations ； Meshless (Mesh-free) ； Finite Volume Method (FVM)

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