利用無限遠域邊界條件求解近域之壩底滲流流場－理論與應用

求解壩體基礎孔隙介質中的滲流情況，通常需取上下游一較遠的區域作為求解範圍，以避免上下游未知的邊界效應影響。然而至今並無明確準則告知多大的範圍才算恰當。於前人的試驗研究與數值模擬中發現上下游端遠距離的邊界影響仍大，不可忽視。以往在求解壩底下有限範圍內之滲流流場，在上下游邊界部分多以定水頭或斜率式方式給定，但其實根本上是未知的物理條件。有鑑於此，本文以半解析解(semi-analytical method)的方式，結合壩體底下近域範圍內的數值解與其下游的解析解來求滲流流場。先求得壩底之下游無限遠域的Laplace方程式解析解之通式，並將此解析解之通式的左邊界（未知水頭函數）離散成無限多項之線性組合，以其斜率式作為近域範圍之下游邊界條件並與近域數值解結合求解出全域之滲流流場。本文除了將近域範圍縮小以驗證半解析法是否正確之外，最後也模擬壩體不透水效應及不規則沖刷坑來跟前人之試驗研究比較及探討。

關鍵字

滲流；拉普拉斯方程式；有限差分法；不規則域；近域；遠域

並列摘要

In order to obtain the seepage flow field under a dam-reservoir system, it is usually acceptable that only a finite domain of near field under the dam is considered. The far field domain, although can be influential, is usually neglected as long as we assume that the near field is large enough. The boundary conditions for the near field is usually Dirichiet or Numman type, which imposes either known values or gradients on the boundary. So far, there is no clear rule to tell that how long of the near field is large enough to neglect the influence from the far away domain. Base on previous experimental studies, the downstream boundary can be very important and must not be overlooked. A semi-analytical method is proposed in this study, in which the analytical solution of the Laplace equation in the far field is solved first and to be included in one boundary condition of the near field utilizing a discretizing technique. A finite difference scheme is employed to solve the seepage flow field in the near field. The method is verified in a rectangular domain and then applied to a near-field case with an irregular geometry.

並列關鍵字

Seepage ； Laplace equation ； Finite difference ； Irregular domain ； Near field ； Far field

國際替代計量

利用無限遠域邊界條件求解近域之壩底滲流流場－理論與應用

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