| Summary: | 碩士 === 國立臺灣海洋大學 === 河海工程學系 === 98 === In recent years, due to the rapid development of the computer technology and academic studies, the knowledge for engineering applications is improved significantly. Therefore, the use of latest technology and knowledge to solve engineering problems is an important issue.
The purpose of this study is to solve groundwater seepage problems using the latest developed method, named the Fictitious Time Integration Method (FTIM). The FTIM was first used to solve a nonlinear system of algebraic equations by introducing fictitious time (Liu and S. N. Atluri, 2008), such that it is a mathematically equivalent system in the augmented n+1-dimensional space as the original algebraic equation system is in the original n- dimensional space. The fixed point of these evolution equations, which is the root for the original algebraic equation, is obtained by applying numerical integrations on the resultant ordinary differential equations, which do not require the information of derivative of nonlinear algebraic equation and their inverse. Since the FTIM has the advantages that it does not need to calculate the Jacobian matrix and its inverse and is thus very time saving, it has great potential for solving groundwater seepage problems.
In this study, the FTIM is incorporated with the finite difference method for solving groundwater seepage problems. Several applications, including two- dimensional confined and unconfined aquifer problems with the consideration of homogenous and non-homogenous, isotropic and anisotropic, and steady-state and transient conditions using the FTIM are conducted. Results obtained demonstrate that with the ease of numerical implementation, the FTIM can easily deal with groundwater seepage problems and has high efficiency as well as high accuracy. In addition, the numerical method developed in this study can also correctly calculate groundwater seepage problems with very large difference of material permeability without any special numerical treatment.
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