| In this thesis, we present an improved finite difference (FD) method for solving complex 2-D groundwater flow problems in anisotropic media. In particular, we address one of the major difficulties in solving the tensorial form of the groundwater flow equation. Traditional FD techniques, when applied to the flow equation containing the complete conductivity tensor, often lead to physically unrealistic results. Traditional FD methods are particularly problematic when the anisotropy is strong and its major orientation deviates significantly from the rectilinear coordinate system. Our new approach eliminates the problem by approximating the tensorial "diffusion" terms in a rotated coordinate system locally aligned with the major direction of anisotropy. It then expresses and interpolates the non-nodal heads in the resulting numerical expression in terms of global nodal heads. The result is a significantly improved scheme that is more accurate and robust than the traditional finite difference scheme. In addition, the new approach is monotonic and always leads to a physically meaningful solution. We demonstrate the advantage of the improved FD approach with a number of groundwater flow examples and a systematic comparison with exact solutions and solutions obtained from traditional FD methods. |
