Improvement on Mass Conservation and Numerical Diffusion for Flow Simulation Model in Unsaturated Zone

• Main Authors: Shu Hue Chu, 褚淑慧
• Other Authors: Keh Chia Yeh
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/60136107732695610566

碩士 === 國立交通大學 === 土木工程系 === 90 === The main purpose of study is to improve mass conservation and numerical diffusion problem for water flow model in unsaturated zone. The 1-D model is solved by finite difference method, and its numerical characteristic is also investigated. This study adopts Celia’s (1990) mixed Richards’ equation and Smolarkiewicz’s (1983) simple positive-definite advection scheme to formulate the mass conservation anti-diffusion equations. After the special treatment of the continuity problem in the unsaturated and saturated buffer zone, this study aims at different finite difference forms of the hydraulic conductivity coefficient in the temporal and spatial domain, mathematical and numerical characteristic, and time interval and grid size. The applicability and influence of those factors for the model are analyzed, and the test and verification of the model are executed by using data from Touma and Vauclin’s (1986) infiltration experiment and Los Almas National Laboratory’s drainage experiment. Numerical results show that anti-diffusion can be achieved by first using Celia’s mass-conservation finite difference method for the linearlized Richards’equation, and then using simple positive-definite advection scheme more than twice to current the numerical diffusion. In addition, the mass is more conserved as the correction times of anti-diffusion increase. Different Forms of the averaged hydraulic conductivity coefficient will significantly affect the advection velocity of the infiltration front; different soils have their respectively suitable averaged forms of the hydraulic conductivity coefficient. Arithmetical average, geometric average, and upstream weighting average of the hydraulic conductivity coefficients have almost the same performance of describing the advection of the infiltration front, but with a slight difference due to different soil composition. The choice of the suitable time step and grid size of the model is on basis of exact solution and root-mean-square error test. Throuth the composition of Havercamp et al.’s (1977) and Touma and Vauclin’s (1986) experimental data shows that and is the better choice. When the advection of the infiltration front is significant, the selection of and has large affect on the numerical diffusion. Variable and will increase the error of estimating the advection of the infiltration front, but the error can be reduced by selecting allowable maximum . From the application and verification study of model, it can be found that advection process is more important than diffusion process when the soil is getting wet (infiltration experiment) and more iterations are required to quarantee the numerical convergence. On the other hand, the advection affect is weaker when the soil is getting dry (drainage experiment), and the model has better performance of convergence. Through the test on the peclet number, the allowable can be obtained. It can be seen that allowable used in the infiltration experiment is smaller than that in the drainage experiment.