發展格點與元素間之交錯網格方法以消除多孔彈性力學之偽震盪問題

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姓名	林宇晨(Yu-Chen Lin) 查詢紙本館藏	畢業系所	機械工程學系
論文名稱	發展格點與元素間之交錯網格方法以消除多孔彈性力學之偽震盪問題
檔案	[Endnote RIS 格式] [Bibtex 格式] [相關文章] [文章引用] [完整記錄] [館藏目錄] 至系統瀏覽論文 (2027-7-31以後開放)
摘要(中)	過去以有限元素方法計算多孔彈性力學問題時，在不可壓縮流體與低滲透率的條件下，模擬結果存在著孔隙壓力數值震盪的問題，該現象不符合真實的物理現象。因此，為了消除此一非物理性的震盪現象(即偽震盪)，本研究提供了一種簡易且基於有限體積的質量守恆與動量守恆概念下的交錯演算法，此方法是將位移變數與孔隙壓力變數在空間上交錯配置進行求解。接著，為了驗證此一方法的可行性，本研究亦對此方法進行收斂分析與探討各項無因次係數對系統穩定性的影響，並針對與其他的數值模擬結果進行相互比較。透過三種不同的物理問題，分析此一交錯方法對數值上的偽震盪現象消除效果。生物組織可以被視為被流體滲透的多孔、可滲透和可變形的介質。將交錯方法運用於多重網絡彈性理論(MPET)中以研究此類生物系統中的傳輸現象。並且利用一個模擬大腦的案例，探討其方法之可行性。
摘要(英)	It is well-known that, under the conditions of incompressible fluid and low permeability, the finite element method results would cause non-physical oscillations in the discrete pressure solution. The oscillations doesn’t correspond to a real physical phenomenon. In order to eliminate the non-physical oscillation, this study propose a staggered finite volume method based on the conservation of mass and the conservation of momentum. This method is solved by method in which the displacement and pore pressure unknowns are located in a staggered configuration. Then, in order to verify the feasibility of this method, this study carried out a convergence analysis of this method. And discuss the influence of each dimensionless coefficients on the system stability, Furthermore, through three different physical problems, analyze the effect of this staggered method on the numerical value of non-physical oscillation elimination. Biological tissue can be viewed as a porous, permeable and deformable medium penetrated by fluids. The staggered method has been developed based on the Multiple-Network Poroelastic Theory (MPET) to study transport phenomena in such biological systems. We proposed a case of simulating cerebral environment to explore the feasibility of its method.
關鍵字(中)	★ 交錯方法 ★ 非物理性震盪 ★ 多重網絡彈性理論	關鍵字(英)	★ staggered method ★ non-physical oscillation ★ MPET
論文目次	中文摘要 i 英文摘要 ii 目錄 iii 圖目錄 v 表目錄 vi 符號說明 vii 第一章緒論 1 1.1 研究動機與目的 1 1.2 文獻回顧 2 1.2.1 多孔彈性力學理論 2 1.2.2 偽震盪問題 2 1.2.3 控制體積有元素法與交錯網格方法 3 1.2.4 多重網絡彈性理論 4 1.3 論文架構 5 第二章數學模型 7 2.1 統御方程式 7 2.1.1 多孔彈性力學模型 7 2.1.2 無因次化方程 8 2.1.3 多重網絡多孔彈性力學模型 9 2.2 數值方法 10 2.2.1 交錯網格方法 10 2.2.2 控制體積有限元素法 11 2.2.3 最小平方重構有限體積法 12 2.2.4 離散方程式 15 第三章結果與討論 18 3.1 數學模型分析 18 3.2 物理模型分析 20 3.2.1 多孔彈振動問題 20 3.2.2 Terzaghi 問題 21 3.2.3 多介質多孔彈分析 23 3.2.4 Mandel 問題 26 3.2.5 圓形狹縫模型模擬 28 3.2.6 大腦6MPET模型模擬 31 第四章結論與未來展望 38 4.1 結論 38 4.2 未來展望 39 參考資料 40
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指導教授	周鼎贏鍾禎元(Dean Chou Chen-Yuan Chung)	審核日期	2022-7-25
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