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題名 | 毛細現象校正式與數值解之比較 |
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作者 | 譚義績; 陳錦松; | 書刊名 | 國立臺灣大學農學院研究報告 |
卷期 | 32:4 1992.12[民81.12] |
頁次 | 頁257-275 |
分類號 | 332.66 |
關鍵詞 | 毛細現象; 校正式; 數值解; 含水層; Capillary phenomenon; Numerical solution; Aquifer; |
語文 | 中文(Chinese) |
中文摘要 | 在非拘限含水層之地下水流公式中,通常假設在流動範圍內之上層邊界 是一個自由表面,此自由表面介於飽和層和末飽和層之間。這樣的假設雖然很簡 便,但是對某些情況來說卻太簡化了;事事上,上層邊界並不是一個很清楚的界 面,而是一個部份飽和的過渡區,亦即毛細現象區。雖然這種流動情況可以用 Richards equatior來描述,但是此方程式的解對實際問題來說並不是那麼容易。因 此,如何尋找一個簡單的方法來計算部份飽和區城內自由表面的公式,是值得研 究的。 本文之研究方法在理論分析方面結合Parlange&Brutsaert(1987)所推導出之毛細現 象校正方程式與Fink(1990)方程式,以不同之邊界起始條件,利用分離變數法求 得其解析解。在數值模擬方面,利用數值之有限差分法,對時間取前差空間取中 央差分(FTCS),將控制方程式化為隱性有限差分形式,並以湯馬士演算法(Thomas Algorithm)求出不同時段之自由水面高度。希望經由理論分析之解析解及數值模 擬結果之比較分析,能對毛細現象有進一步的了解,作為研究地下水之參考。 |
英文摘要 | Traditionally, the groundwater flow equation of unconfined Aquifer is supposed that the upper boundary of flow area is a free surface.This free surface is located between saturated and unsaturated zones.The assumption is very simple and convenient, but for some situationit is over-simplifieid. In fact, the upper boundary is not a sharpinterface but a transitional zone of partially saturated that is acapillary zone. the flow phenomenon can be described by Richardsequation (1931), but the solution is not easy for practical problems. So,it is worthy for study how to find a correction of the free surfaceequation on the partially saturated zone. The research of this study contains two parts; theoretical analysisand numerical simulation. First, a linearlized Boussinesq equationderived the theoretical equation of capillarity. In addition, a numericalmethod adopted fully implicit finite difference for time and centraldifference for space (FTCS) into the governing equation, and solved itby Thomas Algorithm. The purpose of this research is to compare the theoreticialanalysis and numerical simulation for the understanding of capillarybehavior. |
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