Multigrid Approach of Flow Near Groyne

本研究係以多層網格法（Mulitigrid method）配合網格細密化技巧，模擬求解二維、不可壓縮、黏滯性紊流之流體運動問題。以沿水深平均的連續及動量方程為本研究模式之控制方程式，多層網格法係以特定連結的技巧，建立成一適當之資料結構（Data base）之關係架構，其間以一階導數誤差為網格自動細密化之控制指標。控制方程式採用有限差分法(finite difference method)離散處理，並以顯性法(explicit methods)為求解技巧。 本模式應用於模擬黏性紊流遇單一及連續雙丁埧之流場流況，依丁埧後回流區與再接觸點之位置做探討。文中探討在各種雷諾數、束縮比及亂流交換係數條件下之流場變化。討論再接觸點之位置變化，其與試驗值結果作比較。 數值模式則以多層網格法及網格自動細密化技巧，應用於定量及非定量流場之計算，能有效地大量節省計算機容量及時間。且格網之局部自動細密化分佈能偵測流場速度梯度變化大之區域，可以清楚地反應出流場特性。The Multigrid method combining with the automatic, adaptive mesh refinement technique is used to simulate the behaviors of two-dimensional unsteady ,incompressible ,viscous turbulent flow .The governing equations of continuity and momentum are along dapth-averged.The multigrid approach requires a data structure that is simple enough to imple- mentefficiently, yet flexible enough to premit the very complicated patterns of local mesh refinement that would be generated by an adaptive mesh refinement strategy .The adaptive mesh refinement criterion is based on estimates of the first order derivative error .The finite differences method is applied in the models. The model is applied to simulating one or two groins fluid,and discuss the recirculating zone uand positions of reattach point after the groins.In this paper, we discuss the change of flow field with variety difference Reynold number, contraction ratio and turbulent exchange coefficient. And finding the relationship about reattach points position with experimental value results. The model of multigrid approach combined with automatic adaptive refinement technique can produce an efficient and stable solution strategy for solving the steady-state and unsteady-steady incompressible Navier-Stokes equations. Considerable memory savings as well as a reduction in the total CPU time are achieved. To use the local refinement of mesh to detect the locations where sharp velocity gradient exists.目 錄 誌謝I 摘要II AbstractIII 目錄IV 表目錄VI 圖目錄VI 第一章 緒論1 1-1前言1 1-2 研究目的3 第二章 文獻回顧4 第三章 數值理論與方法8 3-1模式概述8 3-2控制方程式8 3-3數值方法11 3-4多層網格法14 3-5非均勻網格之多層網格數值結構15 3-6自動格網細密化16 3-7誤差判斷17 3-7-1能量範數17 3-8漢米內差法20 第四章 模式應用22 4-1河道中設有丁埧之流場模擬22 4-2結果與討論26 4-2-1名詞定義26 4-2-2亂流交換係數Ax對流場之影響26 4-2-2a數值模擬與實驗結果之比較29 4-2-3不同雷諾數下之流場變化31 4-2-4河道束縮對回流區域之影響33 4-2-5連續雙丁埧相互干擾情形34 4-2-6流場誤差變化35 4-2-7多重網格與均勻網格之比較36 第五章 結論與建議38 5-1結論38 5-2建議39 參考文獻41 附錄一4