Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/34952
標題: Application of Local Radial Basis Function Refinement with Finite Element Model in Groundwater Studies
區域化無網格加密技術應用於有限元素地下水數值模式之研究
作者: 沈政泓
Shen, Cheng-Hung
關鍵字: Finite element method
有限元素法
Local radial basis function collocation method
Meshless
Irregular domain
Groundwater equations
區域幅狀基底函數法無網格
不規則形狀
地下水方程式
出版社: 水土保持學系所
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摘要: This study proposed a numerical procedure which is a combination of the finite element method (FEM) and local radial basis function collocation method (LRBFCM). The proposed model was developed to solve the groundwater equation with a complex point seeding system. The present procedure starts with an initial computation by FEM with a coarse mesh. By adopting the initial computational results as the boundary conditions, we employed a meshless numerical technique - LRBFCM to further evaluate the precise solutions by the arbitrarily refined computational nodes in the local area. The converged solutions are able to be obtained by using this numerical procedure via repeatedly superposition. The proposed model is suitable for application in the investigated area that possesses the information on the coarse mesh and the partially measured topographic and geologic data. To avoid the interpolating errors resulting, the coordinates of the coarse mesh can be treated as the initial mesh directly. The partially further measured or probed locations are able to be attached with the refined computational nodes without additional mesh generating. In this thesis, we firstly solved the 2D and 3D Poisson equations by the present numerical procedure. The groundwater level simulations for well-pumping problems are also tested. In order to verify the accuracy, stability and robustness of the proposed model, regular and irregular shaped computational domains were adopted. The steady and unsteady numerical solutions show good agreements with the analytical solutions or reference data. At last, two practical cases are introduced to perform the applications of this study. The simulation results of the proposed model are compared with the measurement data or numerical solutions of reference articles. These applications present reasonable results as well. It demonstrates that the FE-LRBFCM is a satisfactory numerical tool for simulating the groundwater problems.
本研究是發展一個結合有限元素法及區域幅狀基底函數法的數值模式,配合複合型式的計算佈點以求解地下水方程式。在計算域內利用粗疏矩形格點作為初始網格,以有限元素法求得疏網格結果;再以疏網格結果作為邊界條件,配合局部加密的無網格結點,以區域幅狀基底函數法求解細部成果;並經由疏密數值程序反覆疊代求得收斂結果。此模式適合用於具備粗疏格網數值幾何資料,及部份細部測量探勘成果的研究區域,可以直接利用數值幾何資料作為初始網格,避免傳統網格重建時地形地質資訊內插所產生的誤差;局部的細部測量探勘位置亦可直接作為物網格細部計算的結點,可以方便的利用容易取得的計算條件進行精細的數值計算。本文先利用二維及三維的規則形狀與不規則形狀計算域分別求解有理論解的穩態波以松方程式與暫態的擴散方程式,再分別測試穩態的地下水位面在非侷限含水層及抽水井抽水後地下水位洩降的問題,以驗證本模式穩定、精確及適用性。最後並引用兩個實務的案例,以本研究所提出的三維抽水數值模式進行模擬分析,並與參考文獻中的實測資料及數值模擬比較,以驗證本研究所提出的數值模式之實用性。結果顯示有限元素-區域輻狀基底函數模式可以精確的模擬二維及三維的地下水方程式。
URI: http://hdl.handle.net/11455/34952
其他識別: U0005-2308201011044300
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