Numerical Implementation of a Space-Transformation Approach for Solving the Three-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 multidimensional problems by reducing them to unidimensional ones. In particular, the implementation aspects considered in this work include (i) the development and testing of numerical space-transformation algorithms for three-dimensional, space-dependent functions that can be used to model flow within porous media, and (ii) the use of these algorithms to solve partial differential equations governing groundwater flow. We also establish the competitiveness of the spacetransformation-based numerical 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 obtaining three-dimensional flow solutions that honor the boundary conditions. This approach can be also used in stochastic flow modeling to generate multiple realizations of the random hydraulic head field.