| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 87 === The first purpose of this research is to develop a two-dimensional water flow numerical model in the unsaturated zone using the Finite-Analytic Method. After this, we will use the concept of mass balance and a Richard''s equation analytic solution to test and verify the numerical model for the purpose of understanding the influence of numerical stability and accuracy by each influent variable. The test term includes soil type, iteration method, boundary condition design and the time-space local grid combination. The test result shows as following:
1. The numerical model we just develop can correctly simulate the moisture distribution in the unsaturated zone under the condition of neglecting the affection by the boundary condition design. Also, the idea of changing a no-flow boundary condition in the vertical direction with a one-dimensional Finite-Analytic numerical model in the unsaturated zone is available. But in this test experiment, we couldn''t show the help of gaining the numerical stability by using this idea.
2. Line-by-line iteration in different direction would not have any influence upon the result of the numerical computation. Also, in this test experiment, we couldn''t show the influence of numerical stability apparently by using different line-by-line iteration direction. Besides, the difference between linear or non-linear iteration method decreases with the decreasing time interval; but in the same time interval, grid spacing wouldn''t have much influence in the model computation result with using linear or non-linear iteration method. Although linear or non-linear iteration method can also simulate unsaturated zone moisture distribution, but the computation efficiency of non-linear iteration method is worse that the linear iteration method.
3. From the MR (mass balance ratio) trend resulting by the different combination of time-space local grid, they surely have the best combination. But, this trend from the combination of time-space local grid is not one we expect to.
4. The model in our study can also use nine-point non-homogeneous analytic element to simulate the problem of the unsaturated zone. Also, we prove the way of using five-point element to simulate non-regular boundary mesh in the unsaturated zone again.
The preliminary purpose of this study is about keeping on to improve one-dimensional numerical model to promote the computation convergence stability and the computation efficient. The study result shows that the comparison between our improving model with the last developed one, the convergence result almost matches very well. Also, our improving model spend much less CPU computation time than the last developed one and this difference would become bigger as the time interval is getting less. It apparently shows that our improving one-dimensional numerical model can attend the goal we set before.
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