NUMERICAL IMPLEMENTATION OF A SPACE-TRANSFORMATION APPROACH FOR SOLVING THE 3-DIMENSIONAL FLOW EQUATION

This work is concerned with the numerical implementation of the space- transformation approach in porous media modeling. Space transformation is a mathematical approach that simplifies the study of multidimensio nal problems by reducing them to unidimensional ones. In particular, t he implementation aspects considered in this work include (i) the deve lopment and testing of numerical space-transformation algorithms for t hree-dimensional, space-dependent functions that can be used to model flow within porous media, and (ii) the use of these algorithms to solv e partial differential equations governing groundwater flow. We also e stablish the competitiveness of the space-transformation-based numeric al procedures in terms of accuracy and speed. Further improvements in computational speed can be accomplished by parallel implementation of the space-transformation calculations. The space-transformation method is shown to provide a computationally efficient approach for obtainin g three-dimensional flow solutions that honor the boundary conditions. This approach can be also used in stochastic flow modeling to generat e multiple realizations of the random hydraulic head field.