以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：22

、訪客IP：18.222.227.227

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
參考文獻	[1] Terzaghi, K., Erdbaumechanik auf bodenphysikalischer Grundlage. 1925: F. Deuticke. [2] Biot, M.A., General theory of three‐dimensional consolidation. Journal of applied physics, 1941. 12(2): p. 155-164. [3] Biot, M.A., Theory of elasticity and consolidation for a porous anisotropic solid. Journal of applied physics, 1955. 26(2): p. 182-185. [4] Biot, M.A. and D.G. Willis, The elastic coefficients of the theory of consolidation. 1957. [5] Zienkiewicz, O., C. Chang, and P. Bettess, Drained, undrained, consolidating and dynamic behaviour assumptions in soils. Geotechnique, 1980. 30(4): p. 385-395. [6] Ferronato, M., G. Gambolati, and P. Teatini, Ill-conditioning of finite element poroelasticity equations. International Journal of Solids and Structures, 2001. 38(34-35): p. 5995-6014. [7] Bergamaschi, L., M. Ferronato, and G. Gambolati, Mixed constraint preconditioners for the iterative solution of FE coupled consolidation equations. Journal of Computational Physics, 2008. 227(23): p. 9885-9897. [8] Vermeer, P.A. and A. Verruijt, An accuracy condition for consolidation by finite elements. International Journal for Numerical and Analytical Methods in Geomechanics, 1981. 5(1): p. 1-14. [9] Zienkiewicz, O.C., et al., Static and dynamic behaviour of soils : a rational approach to quantitative solutions. I. Fully saturated problems. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1990. 429(1877): p. 285-309. [10] Murad, M.A. and A.F.D. Loula, On stability and convergence of finite element approximations of Biot′s consolidation problem. International Journal for Numerical Methods in Engineering, 1994. 37(4): p. 645-667. [11] Murad, M.A., V. Thomée, and A.F.D. Loula, Asymptotic Behavior of Semidiscrete Finite-Element Approximations of Biot’s Consolidation Problem. SIAM Journal on Numerical Analysis, 1996. 33(3): p. 1065-1083. [12] Wan, J., et al., Stabilized Finite Element Methods for Coupled Geomechanics - Reservoir Flow Simulations, in SPE Reservoir Simulation Symposium. 2003, Society of Petroleum Engineers: Houston, Texas. p. 11. [13] Korsawe, J. and G. Starke, A Least-Squares Mixed Finite Element Method for Biot′s Consolidation Problem in Porous Media. SIAM Journal on Numerical Analysis, 2005. 43(1): p. 318-339. [14] Haga, J.B., H. Osnes, and H.P. Langtangen, On the causes of pressure oscillations in low-permeable and low-compressible porous media. International Journal for Numerical and Analytical Methods in Geomechanics, 2012. 36(12): p. 1507-1522. [15] Huber, R. and R. Helmig, Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media. Computational Geosciences, 2000. 4(2): p. 141-164. [16] Hurtado, F., et al., A Quadrilateral Element-Based Finite-Volume Formulation for the Simulation of Complex Reservoirs. Proceedings of the SPE Latin American and Caribbean Petroleum Engineering Conference, 2007. 2. [17] Durlofsky, L.J., Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities. Water Resources Research, 1994. 30(4): p. 965-973. [18] Cumming, B., T. Moroney, and I. Turner, A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media. BIT Numerical Mathematics, 2011. 51(4): p. 845-864. [19] Nick, H.M. and S.K. Matthäi, Comparison of Three FE-FV Numerical Schemes for Single- and Two-Phase Flow Simulation of Fractured Porous Media. Transport in Porous Media, 2011. 90(2): p. 421-444. [20] Harlow, F.H. and J.E. Welch, Numerical calculation of time‐dependent viscous incompressible flow of fluid with free surface. The physics of fluids, 1965. 8(12): p. 2182-2189. [21] Lilly, D.K., On the computational stability of numerical solutions of time-dependent non-linear geophysical fluid dynamics problems. Monthly Weather Review, 1965. 93(1): p. 11-25. [22] Boal, N., et al., Finite-difference analysis of fully dynamic problems for saturated porous media. Journal of Computational and Applied Mathematics, 2011. 236(6): p. 1090-1102. [23] Sokolova, I., M.G. Bastisya, and H. Hajibeygi, Multiscale finite volume method for finite-volume-based simulation of poroelasticity. Journal of Computational Physics, 2019. 379: p. 309-324. [24] Kadeethum, T., et al., Enriched Galerkin discretization for modeling poroelasticity and permeability alteration in heterogeneous porous media. Journal of Computational Physics, 2021. 427: p. 110030. [25] Maliska, C.R., H.T. Honório, and J. Coelho Jr. A non-oscillatory staggered grid algorithm for the pressure-displacement coupling in geomechanics. in IACM 19th international conference in flow problems–FEF. 2017. [26] Bai, M., D. Elsworth, and J.C. Roegiers, Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs. Water Resources Research, 1993. 29(6): p. 1621-1633. [27] Tully, B. and Y. Ventikos, Cerebral water transport using multiple-network poroelastic theory: application to normal pressure hydrocephalus. Journal of Fluid Mechanics, 2011. 667: p. 188-215. [28] Chou, D., Computational modelling of brain transport phenomena: application of multicompartmental poroelasticity. 2016, University of Oxford. [29] Wang, H.F., Theory of linear poroelasticity with applications to geomechanics and hydrogeology. 2017: Princeton University Press. [30] Verruijt, A., Theory and problems of poroelasticity. Delft University of Technology, 2013. 71. [31] Mandel, J., Consolidation des sols (étude mathématique). Geotechnique, 1953. 3(7): p. 287-299. [32] Abousleiman, Y., et al., Mandel′s problem revisited. Geotechnique, 1996. 46(2): p. 187-195.
指導教授	周鼎贏 鍾禎元(Dean Chou Chen-Yuan Chung)	審核日期	2022-7-25
推文	facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu
網路書籤	Google bookmarks   del.icio.us   hemidemi   myshare