ALE寬頻元素法於不可壓縮流之發展與應用

Abstract

本文的主要目的在於發展ALE法的寬頻元素法用於處理具移動邊界的不可壓縮流問題，並應用此工具於流-固相互作用的研究。統御方程式的運動描述法採用ALE法是為了有效處理邊界的移動與減少網格的扭曲，而空間離散所採用的寬頻元素法具有高精確度的特性，在同一個數值精確度下需要計算的自由度比低階的方法相對來的少，程式上要處理的資料也就比較少，有助於提高流場的程式效率也有利於動態網格的應用，且使用的網格也可較大，可減輕網格的扭曲問題；本文以一維、二維的伯格方程式及二維不可壓縮之Navier-Stokes方程式驗證、討論程式的正確性與移動網格對數值收斂的影響；在實例的應用上，將會測試、討論三個例子，包括凹陷移動的管內流、流體流經一橫向振動圓柱與流體流經兩並肩排列橫向振動圓柱，前兩個例子在趨勢與大小上都與文獻的模擬結果符合，確認本文所發展的工具於實際問題的可靠性，最後用於觀察兩並肩排列橫向振動圓柱的現象，除數值結果的討論外，並與實驗結果比較同異之處。

The main purpose of this thesis is to develop a spectral element method based on the ALE formulation for incompressible flow with moving boundary problems and present the application for fluid-structure interaction problem. Arbitrary Lagrangian Eulerian(ALE) formulation can offer robust treatment of the moving boundary and handle distortions of the computational mesh. Spectral element method, delivering high-order convergence characteristics, allow utilization of relatively fewer degrees of freedom than low-order methods for a desired accuracy. This is an advantage in reduction of data,efficiency of the algorithms and the application of dynamic mesh. Also, relatively larger elements than low-order methods enables spectral element ALE algorithms to reduce the problem of distortions. One dimensional and two dimensional Burger’s equation, incompressible two dimensional Navier-Stokes equation are applied to test the numerical accuracy and the effect of moving mesh on numerical convergence. The following two examples, flow in a channel with a moving indentation and flow past an transverse oscillating cylinder, show quantitative agreement with the numerical results and demonstrate the effectiveness of the method in some of these application. Detailed results are presented for last case, flow past an transverse oscillating cylinder, and preliminarily compared with the experimental results.